Question 1

Write the form of the partial fraction decomposition of the rational expression.Do not solve for the constants.​ $$\frac { 5 } { x ^ { 3 } - 2 x ^ { 2 } }$$ ​

Accepted Answer

A)  $\frac { A } { x ^ { 2 } } + \frac { B } { x ^ { 3 } } + \frac { C } { x - 2 }$ 
B)  $\frac { A } { x } + \frac { B } { x ^ { 2 } } + \frac { C } { x - 2 }$ 
C)  $\frac { A } { x } + \frac { B } { x ^ { 3 } } + \frac { C } { x ^ { 2 } - 2 }$ 
D)  $\frac { A } { x ^ { 2 } } - \frac { B } { x ^ { 3 } } - \frac { C } { x - 2 x ^ { 2 } }$ 
E)  $\frac { A } { x ^ { 2 } } + \frac { B } { x ^ { 2 } - 2 }$ 
A)  $\frac { A } { x ^ { 2 } } + \frac { B } { x ^ { 3 } } + \frac { C } { x - 2 }$ 
B)  $\frac { A } { x } + \frac { B } { x ^ { 2 } } + \frac { C } { x - 2 }$ 
C)  $\frac { A } { x } + \frac { B } { x ^ { 3 } } + \frac { C } { x ^ { 2 } - 2 }$ 
D)  $\frac { A } { x ^ { 2 } } - \frac { B } { x ^ { 3 } } - \frac { C } { x - 2 x ^ { 2 } }$ 
E)  $\frac { A } { x ^ { 2 } } + \frac { B } { x ^ { 2 } - 2 }$ B

Question 2

Write the form of the partial fraction decomposition of the rational expression.Do not solve for the constants.​ $$\frac { 5 x + 4 } { ( x + 2 ) ^ { 4 } }$$ ​

Accepted Answer

A)  $\frac { A } { ( x + 2 ) ^ { 2 } } + \frac { B } { ( x + 2 ) ^ { 3 } } + \frac { C } { ( x + 2 ) ^ { 4 } }$ 
B)  $\frac { A } { ( x + 2 ) ^ { 4 } }$ 
C)  $\frac { 5 } { x + 2 } - \frac { 4 } { ( x + 2 ) ^ { 2 } } - \frac { 2 } { ( x + 2 ) ^ { 3 } } - \frac { 4 } { ( x + 2 ) ^ { 4 } }$ 
D)  $\frac { A } { ( x + 2 ) ^ { 2 } } + \frac { B } { ( x + 2 ) ^ { 2 } }$ 
E)  $\frac { A } { x + 2 } + \frac { B } { ( x + 2 ) ^ { 2 } } + \frac { C } { ( x + 2 ) ^ { 3 } } + \frac { D } { ( x + 2 ) ^ { 4 } }$ 
A)  $\frac { A } { ( x + 2 ) ^ { 2 } } + \frac { B } { ( x + 2 ) ^ { 3 } } + \frac { C } { ( x + 2 ) ^ { 4 } }$ 
B)  $\frac { A } { ( x + 2 ) ^ { 4 } }$ 
C)  $\frac { 5 } { x + 2 } - \frac { 4 } { ( x + 2 ) ^ { 2 } } - \frac { 2 } { ( x + 2 ) ^ { 3 } } - \frac { 4 } { ( x + 2 ) ^ { 4 } }$ 
D)  $\frac { A } { ( x + 2 ) ^ { 2 } } + \frac { B } { ( x + 2 ) ^ { 2 } }$ 
E)  $\frac { A } { x + 2 } + \frac { B } { ( x + 2 ) ^ { 2 } } + \frac { C } { ( x + 2 ) ^ { 3 } } + \frac { D } { ( x + 2 ) ^ { 4 } }$ E

Question 3

Write the form of the partial fraction decomposition of the rational expression.Do not solve for the constants. $\frac { x + 5 } { x \left( x ^ { 2 } + 6 \right) ^ { 2 } }$

Accepted Answer

A)  $\frac { A } { x } + \frac { B x + C } { \left( x ^ { 2 } + 6 \right) ^ { 2 } }$ 
B)  $\frac { A x + B } { x ^ { 2 } + 6 } + \frac { C x + D } { \left( x ^ { 2 } + 6 \right) ^ { 2 } }$ 
C)  $\frac { A } { x } + \frac { B x + C } { x ^ { 2 } + 6 } + \frac { D x + E } { \left( x ^ { 2 } + 6 \right) ^ { 2 } }$ 
D)  $\frac { A x + B } { x } + \frac { C x + D } { x ^ { 2 } + 6 } + \frac { E x + F } { \left( x ^ { 2 } + 6 \right) ^ { 2 } }$ 
E)  $\frac { A } { x } + \frac { B } { x ^ { 2 } + 6 } + \frac { C } { \left( x ^ { 2 } + 6 \right) ^ { 2 } }$ 
A)  $\frac { A } { x } + \frac { B x + C } { \left( x ^ { 2 } + 6 \right) ^ { 2 } }$ 
B)  $\frac { A x + B } { x ^ { 2 } + 6 } + \frac { C x + D } { \left( x ^ { 2 } + 6 \right) ^ { 2 } }$ 
C)  $\frac { A } { x } + \frac { B x + C } { x ^ { 2 } + 6 } + \frac { D x + E } { \left( x ^ { 2 } + 6 \right) ^ { 2 } }$ 
D)  $\frac { A x + B } { x } + \frac { C x + D } { x ^ { 2 } + 6 } + \frac { E x + F } { \left( x ^ { 2 } + 6 \right) ^ { 2 } }$ 
E)  $\frac { A } { x } + \frac { B } { x ^ { 2 } + 6 } + \frac { C } { \left( x ^ { 2 } + 6 \right) ^ { 2 } }$ C

Question 4

The predicted cost C (in thousands of dollars)for a company to remove p% of a chemical from its waste water is given by the model​ $C = \frac { 124 p } { 90,000 - p ^ { 2 } } , 0 \leq p < 100$ . ​
Write the partial fraction decomposition for the rational function.Verify your result by using the table feature of a graphing utility to create a table comparing the original function with the partial fractions.
​

Accepted Answer

A)  $\frac { 1 } { 300 - p } - \frac { 1 } { 300 + p }$ 
B)  $\frac { 124 } { 300 - p } - \frac { 124 } { 300 + p }$ 
C)  $\frac { 62 } { 300 - p } - \frac { 62 } { ( 300 - p ) ^ { 2 } }$ 
D)  $\frac { 62 } { 300 - p } - \frac { 62 } { 300 + p }$ 
E)  $\frac { 62 } { 300 - p } + \frac { 62 } { 300 + p }$ 
A)  $\frac { 1 } { 300 - p } - \frac { 1 } { 300 + p }$ 
B)  $\frac { 124 } { 300 - p } - \frac { 124 } { 300 + p }$ 
C)  $\frac { 62 } { 300 - p } - \frac { 62 } { ( 300 - p ) ^ { 2 } }$ 
D)  $\frac { 62 } { 300 - p } - \frac { 62 } { 300 + p }$ 
E)  $\frac { 62 } { 300 - p } + \frac { 62 } { 300 + p }$

Question 5

Write the partial fraction decomposition of the rational expression.​ $\frac { 5 - x } { 2 x ^ { 2 } + x - 1 }$ ​

Accepted Answer

A)  $\frac { 3 } { 2 x - 1 } - \frac { 2 } { x + 1 }$ 
B) ​ $\frac { 3 } { 2 x + 1 } + \frac { 2 } { x + 1 }$ 
C)  $\frac { 3 } { 2 x - 1 } - \frac { 2 } { x - 1 }$ 
D)  $\frac { 3 } { 2 x - 1 } + \frac { 2 } { x + 1 }$ 
E)  $\frac { 3 } { 2 x + 1 } - \frac { 2 } { x + 1 }$ 
A)  $\frac { 3 } { 2 x - 1 } - \frac { 2 } { x + 1 }$ 
B) ​ $\frac { 3 } { 2 x + 1 } + \frac { 2 } { x + 1 }$ 
C)  $\frac { 3 } { 2 x - 1 } - \frac { 2 } { x - 1 }$ 
D)  $\frac { 3 } { 2 x - 1 } + \frac { 2 } { x + 1 }$ 
E)  $\frac { 3 } { 2 x + 1 } - \frac { 2 } { x + 1 }$

Question 6

Write the partial fraction decomposition of the rational expression. $\frac { 1 } { 16 x ^ { 2 } - 121 }$

Accepted Answer

A)  $\frac { 1 } { 22 } \left( \frac { 1 } { 4 x - 11 } - \frac { 1 } { 4 x + 11 } \right)$ 
B)  $\frac { 1 } { 11 } \left( \frac { 1 } { 4 x - 11 } - \frac { 1 } { 4 x + 11 } \right)$ 
C)  $$\frac { 1 } { 4 x ^ { 2 } } - \frac { 1 } { 121 }$$ 
D)  $\frac { 1 } { 22 } \left( \frac { x - 4 } { 4 x - 11 } - \frac { x - 4 } { 4 x + 11 } \right)$ 
E)  $\frac { 1 } { 11 } \left( \frac { 1 } { 4 x + 11 } - \frac { 1 } { 4 x - 11 } \right)$ 
A)  $\frac { 1 } { 22 } \left( \frac { 1 } { 4 x - 11 } - \frac { 1 } { 4 x + 11 } \right)$ 
B)  $\frac { 1 } { 11 } \left( \frac { 1 } { 4 x - 11 } - \frac { 1 } { 4 x + 11 } \right)$ 
C)  $$\frac { 1 } { 4 x ^ { 2 } } - \frac { 1 } { 121 }$$ 
D)  $\frac { 1 } { 22 } \left( \frac { x - 4 } { 4 x - 11 } - \frac { x - 4 } { 4 x + 11 } \right)$ 
E)  $\frac { 1 } { 11 } \left( \frac { 1 } { 4 x + 11 } - \frac { 1 } { 4 x - 11 } \right)$

Question 7

Determine whether the statement is true or false.Justify your answer. ​
For the rational expression $\frac{x} { ( x + 60 ) ( x - 60 ) ^ { 2 } }$ the partial fraction decomposition is of the form $\frac { A } { x + 60 } + \frac { B } { ( x - 60 ) ^ { 2 } }$ .
​
​

Accepted Answer

A) False.The partial fraction decomposition is $\frac { A } { x + 60 } + \frac { B } { x - 60 } + \frac { C } { ( x - 60 ) ^ { 2 } }$ . 
B) True 
A) False.The partial fraction decomposition is $\frac { A } { x + 60 } + \frac { B } { x - 60 } + \frac { C } { ( x - 60 ) ^ { 2 } }$ . 
B) True

Question 8

Write the form of the partial fraction decomposition of the rational expression.​ $$\frac { 5 x - 1 } { x ^ { 2 } ( x - 7 ) }$$ ​

Accepted Answer

A)  $\frac { A } { x } + \frac { B } { x ^ { 2 } } + \frac { C x + D } { x - 7 }$ 
B)  $\frac { A } { x ^ { 2 } } + \frac { B } { x + 7 }$ 
C)  $\frac { A } { x ^ { 2 } } + \frac { B x + C } { x + 7 }$ 
D)  $\frac { A x + B } { x } + \frac { C x + D } { x + 7 }$ 
E)  $\frac { A } { x } + \frac { B } { x ^ { 2 } } + \frac { C } { x - 7 }$ 
A)  $\frac { A } { x } + \frac { B } { x ^ { 2 } } + \frac { C x + D } { x - 7 }$ 
B)  $\frac { A } { x ^ { 2 } } + \frac { B } { x + 7 }$ 
C)  $\frac { A } { x ^ { 2 } } + \frac { B x + C } { x + 7 }$ 
D)  $\frac { A x + B } { x } + \frac { C x + D } { x + 7 }$ 
E)  $\frac { A } { x } + \frac { B } { x ^ { 2 } } + \frac { C } { x - 7 }$

Question 9

Write the form of the partial fraction decomposition of the rational expression.Do not solve for the constants.​ $$\frac { x + 2 } { x ^ { 2 } ( 3 x - 8 ) ^ { 2 } }$$ ​

Accepted Answer

A)  $\frac { A } { x + 2 } + \frac { B } { x ^ { 2 } + 8 } + \frac { C } { 3 x - 8 } + \frac { D } { ( 3 x + 8 ) ^ { 2 } }$ ​ 
B) ​ $$\frac { A } { x - 2 } - \frac { B } { x ^ { 2 } } - \frac { C } { x ^ { 2 } ( 3 x - 8 ) } - \frac { D } { ( 3 x - 8 ) ^ { 2 } }$$ ​ 
C)  $\frac { A } { x + 2 } + \frac { B } { x ^ { 2 } } + \frac { C } { ( 3 x - 8 ) ^ { 2 } }$ ​ 
D)  $$\frac { A } { x ^ { 2 } } + \frac { C } { ( 3 x - 8 ) ^ { 3 } } + \frac { D } { ( 3 x - 8 ) ^ { 3 } }$$ ​ 
E)  $\frac { A } { x } + \frac { B } { x ^ { 2 } } + \frac { C } { 3 x - 8 } + \frac { D } { ( 3 x - 8 ) ^ { 2 } }$ 
A)  $\frac { A } { x + 2 } + \frac { B } { x ^ { 2 } + 8 } + \frac { C } { 3 x - 8 } + \frac { D } { ( 3 x + 8 ) ^ { 2 } }$ ​ 
B) ​ $$\frac { A } { x - 2 } - \frac { B } { x ^ { 2 } } - \frac { C } { x ^ { 2 } ( 3 x - 8 ) } - \frac { D } { ( 3 x - 8 ) ^ { 2 } }$$ ​ 
C)  $\frac { A } { x + 2 } + \frac { B } { x ^ { 2 } } + \frac { C } { ( 3 x - 8 ) ^ { 2 } }$ ​ 
D)  $$\frac { A } { x ^ { 2 } } + \frac { C } { ( 3 x - 8 ) ^ { 3 } } + \frac { D } { ( 3 x - 8 ) ^ { 3 } }$$ ​ 
E)  $\frac { A } { x } + \frac { B } { x ^ { 2 } } + \frac { C } { 3 x - 8 } + \frac { D } { ( 3 x - 8 ) ^ { 2 } }$

Question 10

Write the form of the partial fraction decomposition of the rational expression.​ $$\frac { 6 x - 1 } { x \left( x ^ { 2 } - 16 \right) }$$ ​

Accepted Answer

A)  $\frac { A } { x } + \frac { B } { x ^ { 2 } } + \frac { C x + D } { x ^ { 2 } - 16 }$ 
B)  $\frac { A } { 6 x } + \frac { B x + C } { 6 ( x + 4 ) } + \frac { C x + D } { 6 ( x - 4 ) }$ 
C)  $\frac { A } { x } + \frac { B } { x ^ { 2 } } + \frac { C x + D } { x - 16 }$ 
D)  $\frac { A } { x } + \frac { B } { x + 4 } + \frac { C } { x - 4 }$ 
E)  $\frac { A } { x } - \frac { B } { ( x + 16 ) ( x - 16 ) }$ 
A)  $\frac { A } { x } + \frac { B } { x ^ { 2 } } + \frac { C x + D } { x ^ { 2 } - 16 }$ 
B)  $\frac { A } { 6 x } + \frac { B x + C } { 6 ( x + 4 ) } + \frac { C x + D } { 6 ( x - 4 ) }$ 
C)  $\frac { A } { x } + \frac { B } { x ^ { 2 } } + \frac { C x + D } { x - 16 }$ 
D)  $\frac { A } { x } + \frac { B } { x + 4 } + \frac { C } { x - 4 }$ 
E)  $\frac { A } { x } - \frac { B } { ( x + 16 ) ( x - 16 ) }$

Question 11

Write the form of the partial fraction decomposition of the rational expression.Do not solve for the constants. $\frac { 1 } { x ^ { 2 } + 2 x }$

Accepted Answer

A)  $\frac { A x } { x ^ { 2 } } + \frac { B x } { x + 2 }$ 
B)  $\frac { A } { x } + \frac { B x } { x + 2 }$ 
C)  $\frac { A } { x ^ { 2 } } + \frac { B } { x + 2 }$ 
D)  $\frac { A } { x } + \frac { B } { x + 2 }$ 
E)  $\frac { A } { x } - \frac { B x } { x + 2 }$ 
A)  $\frac { A x } { x ^ { 2 } } + \frac { B x } { x + 2 }$ 
B)  $\frac { A } { x } + \frac { B x } { x + 2 }$ 
C)  $\frac { A } { x ^ { 2 } } + \frac { B } { x + 2 }$ 
D)  $\frac { A } { x } + \frac { B } { x + 2 }$ 
E)  $\frac { A } { x } - \frac { B x } { x + 2 }$

Question 12

Write the partial fraction decomposition of the rational expression.​ $\frac { 3 x ^ { 2 } + 3 x + 18 } { \left( x ^ { 2 } + 6 \right) ^ { 2 } }$ ​

Accepted Answer

A)  $\frac { 3 x + 3 } { \left( x ^ { 2 } + 6 \right) ^ { 2 } }$ 
B)  $\frac { 3 } { x ^ { 2 } + 6 } - \frac { 3 x } { \left( x ^ { 2 } + 6 \right) ^ { 2 } }$ 
C)  $\frac { 3 } { x ^ { 2 } + 6 } + \frac { 3 x } { \left( x ^ { 2 } + 6 \right) ^ { 2 } }$ 
D)  $\frac { 3 x + 18 } { x ^ { 2 } + 6 } + \frac { 3 x } { \left( x ^ { 2 } + 6 \right) ^ { 2 } }$ 
E)  $\frac { 3 } { x ^ { 2 } + 6 } + \frac { 3 } { \left( x ^ { 2 } + 6 \right) ^ { 2 } }$ 
A)  $\frac { 3 x + 3 } { \left( x ^ { 2 } + 6 \right) ^ { 2 } }$ 
B)  $\frac { 3 } { x ^ { 2 } + 6 } - \frac { 3 x } { \left( x ^ { 2 } + 6 \right) ^ { 2 } }$ 
C)  $\frac { 3 } { x ^ { 2 } + 6 } + \frac { 3 x } { \left( x ^ { 2 } + 6 \right) ^ { 2 } }$ 
D)  $\frac { 3 x + 18 } { x ^ { 2 } + 6 } + \frac { 3 x } { \left( x ^ { 2 } + 6 \right) ^ { 2 } }$ 
E)  $\frac { 3 } { x ^ { 2 } + 6 } + \frac { 3 } { \left( x ^ { 2 } + 6 \right) ^ { 2 } }$

Question 13

Write the partial fraction decomposition of the rational expression.Check your result algebraically.​ $$\frac { 5 } { x ^ { 2 } + 5 x }$$ ​

Accepted Answer

A)  $\frac { A } { x } + \frac { B } { x - 5 }$ 
B)  $\frac { 1 } { x } - \frac { 1 } { x + 5 }$ 
C)  $\frac { 1 } { x } + \frac { 1 } { x + 5 }$ 
D)  $\frac { A } { x } - \frac { B } { x - 5 }$ 
E)  $\frac { 1 } { x } - \frac { 1 } { x - 5 }$ 
A)  $\frac { A } { x } + \frac { B } { x - 5 }$ 
B)  $\frac { 1 } { x } - \frac { 1 } { x + 5 }$ 
C)  $\frac { 1 } { x } + \frac { 1 } { x + 5 }$ 
D)  $\frac { A } { x } - \frac { B } { x - 5 }$ 
E)  $\frac { 1 } { x } - \frac { 1 } { x - 5 }$

Question 14

Write the partial fraction decomposition of the rational expression.Check your result algebraically.​ $\frac { 2 x } { ( x - 2 ) ^ { 2 } }$ ​

Accepted Answer

A)  $\frac { 2 } { x - 2 } - \frac { 4 } { x - 2 }$ 
B)  $\frac { 2 } { x - 2 } + \frac { 4 } { ( x - 2 ) ^ { 2 } }$ 
C)  $\frac { 2 } { x - 2 } + \frac { 2 } { x - 2 }$ 
D)  $\frac { 2 } { x - 2 } + \frac { 4 } { ( x - 2 ) ^ { 3 } }$ 
E)  $\frac { 2 } { x - 2 } - \frac { 4 } { ( x - 2 ) ^ { 2 } }$ 
A)  $\frac { 2 } { x - 2 } - \frac { 4 } { x - 2 }$ 
B)  $\frac { 2 } { x - 2 } + \frac { 4 } { ( x - 2 ) ^ { 2 } }$ 
C)  $\frac { 2 } { x - 2 } + \frac { 2 } { x - 2 }$ 
D)  $\frac { 2 } { x - 2 } + \frac { 4 } { ( x - 2 ) ^ { 3 } }$ 
E)  $\frac { 2 } { x - 2 } - \frac { 4 } { ( x - 2 ) ^ { 2 } }$

Question 15

Write the partial fraction decomposition of the rational expression.Check your result algebraically.​ $\frac { 1 } { 25 x ^ { 2 } - 36 }$ ​

Accepted Answer

A)  $\frac { 1 } { 12 } \left( \frac { 12 } { 5 x - 6 } - \frac { 12 } { 5 x + 6 } \right)$ 
B)  $\frac { 1 } { 5 x - 6 } - \frac { 1 } { 5 x + 6 }$ 
C)  $\frac { 1 } { 12 } \left( \frac { 1 } { 5 x - 6 } + \frac { 1 } { 5 x + 6 } \right)$ 
D)  $\frac { 1 } { 12 } \left( \frac { 12 A } { 5 x - 6 } - \frac { 12 B } { 5 x + 6 } \right)$ 
E)  $\frac { 1 } { 12 } \left( \frac { 1 } { 5 x - 6 } - \frac { 1 } { 5 x + 6 } \right)$ 
A)  $\frac { 1 } { 12 } \left( \frac { 12 } { 5 x - 6 } - \frac { 12 } { 5 x + 6 } \right)$ 
B)  $\frac { 1 } { 5 x - 6 } - \frac { 1 } { 5 x + 6 }$ 
C)  $\frac { 1 } { 12 } \left( \frac { 1 } { 5 x - 6 } + \frac { 1 } { 5 x + 6 } \right)$ 
D)  $\frac { 1 } { 12 } \left( \frac { 12 A } { 5 x - 6 } - \frac { 12 B } { 5 x + 6 } \right)$ 
E)  $\frac { 1 } { 12 } \left( \frac { 1 } { 5 x - 6 } - \frac { 1 } { 5 x + 6 } \right)$

Question 16

Write the partial fraction decomposition of the rational expression.Check your result algebraically.​ $\frac { 4 x ^ { 2 } + 3 x + 20 } { \left( x ^ { 2 } + 5 \right) ^ { 2 } }$ ​

Accepted Answer

A)  $\frac { 4 } { x ^ { 2 } + 5 } + \frac { 3 } { \left( x ^ { 2 } + 5 \right) ^ { 2 } }$ 
B)  $\frac { 4 x + 20 } { x ^ { 2 } + 5 } + \frac { 3 x } { \left( x ^ { 2 } + 5 \right) ^ { 2 } }$ 
C)  $\frac { 3 x + 4 } { \left( x ^ { 2 } + 5 \right) ^ { 2 } }$ 
D)  $\frac { 4 } { x ^ { 2 } + 5 } - \frac { 3 x } { \left( x ^ { 2 } + 5 \right) ^ { 2 } }$ 
E)  $\frac { 4 } { x ^ { 2 } + 5 } + \frac { 3 x } { \left( x ^ { 2 } + 5 \right) ^ { 2 } }$ 
A)  $\frac { 4 } { x ^ { 2 } + 5 } + \frac { 3 } { \left( x ^ { 2 } + 5 \right) ^ { 2 } }$ 
B)  $\frac { 4 x + 20 } { x ^ { 2 } + 5 } + \frac { 3 x } { \left( x ^ { 2 } + 5 \right) ^ { 2 } }$ 
C)  $\frac { 3 x + 4 } { \left( x ^ { 2 } + 5 \right) ^ { 2 } }$ 
D)  $\frac { 4 } { x ^ { 2 } + 5 } - \frac { 3 x } { \left( x ^ { 2 } + 5 \right) ^ { 2 } }$ 
E)  $\frac { 4 } { x ^ { 2 } + 5 } + \frac { 3 x } { \left( x ^ { 2 } + 5 \right) ^ { 2 } }$

Question 17

Write the form of the partial fraction decomposition of the rational expression.Do not solve for the constants.​ $$\frac { x - 3 } { 6 x ^ { 3 } + 24 x }$$ ​

Accepted Answer

A)  $\frac { x - 3 } { 6 x ^ { 3 } } + \frac { B } { 24 x }$ 
B)  $\frac { A } { 6 x } + \frac { B } { 6 x ^ { 2 } } + \frac { C } { 4 x }$ 
C)  $\frac { A } { 6 x } - \frac { B x + C } { x ^ { 2 } + 4 } + \frac { D } { 6 x ^ { 3 } + 24 x }$ 
D)  $\frac { A } { 6 x } + \frac { B x + C } { x ^ { 2 } + 4 }$ 
E)  $\frac { A } { 6 x } + \frac { B } { x + 4 } + \frac { C } { x + 4 }$ 
A)  $\frac { x - 3 } { 6 x ^ { 3 } } + \frac { B } { 24 x }$ 
B)  $\frac { A } { 6 x } + \frac { B } { 6 x ^ { 2 } } + \frac { C } { 4 x }$ 
C)  $\frac { A } { 6 x } - \frac { B x + C } { x ^ { 2 } + 4 } + \frac { D } { 6 x ^ { 3 } + 24 x }$ 
D)  $\frac { A } { 6 x } + \frac { B x + C } { x ^ { 2 } + 4 }$ 
E)  $\frac { A } { 6 x } + \frac { B } { x + 4 } + \frac { C } { x + 4 }$

Question 18

Write the form of the partial fraction decomposition of the rational expression.Do not solve for the constants.​ $$\frac { x - 3 } { x ^ { 2 } + 7 x + 12 }$$ ​

Accepted Answer

A)  $\frac { 3 } { x + 3 } + \frac { 3 } { x + 4 } + \frac { 3 } { x + 3 }$ 
B)  $\frac { 1 } { x + 3 } + \frac { 1 } { x + 4 }$ 
C)  $\frac { A } { x + 3 } - \frac { B } { x + 4 } + \frac { C } { x + 3 }$ 
D)  $\frac { A } { x - 3 } - \frac { B } { x - 4 } + \frac { C } { x - 4 }$ 
E)  $\frac { A } { x + 3 } + \frac { B } { x + 4 }$ 
A)  $\frac { 3 } { x + 3 } + \frac { 3 } { x + 4 } + \frac { 3 } { x + 3 }$ 
B)  $\frac { 1 } { x + 3 } + \frac { 1 } { x + 4 }$ 
C)  $\frac { A } { x + 3 } - \frac { B } { x + 4 } + \frac { C } { x + 3 }$ 
D)  $\frac { A } { x - 3 } - \frac { B } { x - 4 } + \frac { C } { x - 4 }$ 
E)  $\frac { A } { x + 3 } + \frac { B } { x + 4 }$

Question 19

Write the partial fraction decomposition of the rational expression.Check your result algebraically.​ $\frac { 5 x ^ { 2 } + 3 x - 1 } { x ^ { 2 } ( x + 1 ) }$ ​

Accepted Answer

A)  $- \frac { 4 } { x } - \frac { 1 } { x ^ { 2 } } - \frac { 1 } { x - 1 }$ 
B)  $\frac { 4 } { x } - \frac { 1 } { x ^ { 2 } } - \frac { 1 } { x + 1 }$ 
C)  $- \frac { 4 } { x } - \frac { 1 } { x ^ { 2 } } + \frac { 1 } { x - 1 }$ 
D)  $\frac { 4 } { x } + \frac { 1 } { x ^ { 2 } } + \frac { 1 } { x + 1 }$ 
E)  $\frac { 4 } { x } - \frac { 1 } { x ^ { 2 } } + \frac { 1 } { x + 1 }$ 
A)  $- \frac { 4 } { x } - \frac { 1 } { x ^ { 2 } } - \frac { 1 } { x - 1 }$ 
B)  $\frac { 4 } { x } - \frac { 1 } { x ^ { 2 } } - \frac { 1 } { x + 1 }$ 
C)  $- \frac { 4 } { x } - \frac { 1 } { x ^ { 2 } } + \frac { 1 } { x - 1 }$ 
D)  $\frac { 4 } { x } + \frac { 1 } { x ^ { 2 } } + \frac { 1 } { x + 1 }$ 
E)  $\frac { 4 } { x } - \frac { 1 } { x ^ { 2 } } + \frac { 1 } { x + 1 }$

Question 20

Write the form of the partial fraction decomposition of the rational expression.Do not solve for the constants.​ $$\frac { 4 } { x ^ { 2 } - 3 x }$$ ​

Accepted Answer

A)  $$\frac { A } { x } + \frac { B } { x - 3 }$$ 
B)  $\frac { A } { x } + \frac { B } { 4 ( x + 3 ) }$ 
C)  $$\frac { 1 } { x } + \frac { 1 } { x - 3 } + \frac { 1 } { x + 3 }$$ 
D)  $\frac { A } { x ^ { 2 } - 3 x } + \frac { B } { 4 ( x - 4 ) }$ 
E)  $\frac { A } { 4 x } - \frac { B } { x - 3 }$ 
A)  $$\frac { A } { x } + \frac { B } { x - 3 }$$ 
B)  $\frac { A } { x } + \frac { B } { 4 ( x + 3 ) }$ 
C)  $$\frac { 1 } { x } + \frac { 1 } { x - 3 } + \frac { 1 } { x + 3 }$$ 
D)  $\frac { A } { x ^ { 2 } - 3 x } + \frac { B } { 4 ( x - 4 ) }$ 
E)  $\frac { A } { 4 x } - \frac { B } { x - 3 }$

Exam 44: Partial Fractions

Write the form of the partial fraction decomposition of the rational expression.Do not solve for the constants.​ 5x3−2x2\frac { 5 } { x ^ { 3 } - 2 x ^ { 2 } }x3−2x25​ ​

Write the form of the partial fraction decomposition of the rational expression.Do not solve for the constants.​ 5x+4(x+2)4\frac { 5 x + 4 } { ( x + 2 ) ^ { 4 } }(x+2)45x+4​ ​

Write the form of the partial fraction decomposition of the rational expression.Do not solve for the constants. x+5x(x2+6)2\frac { x + 5 } { x \left( x ^ { 2 } + 6 \right) ^ { 2 } }x(x2+6)2x+5​

Write the partial fraction decomposition of the rational expression.​ 5−x2x2+x−1\frac { 5 - x } { 2 x ^ { 2 } + x - 1 }2x2+x−15−x​ ​

Write the partial fraction decomposition of the rational expression. 116x2−121\frac { 1 } { 16 x ^ { 2 } - 121 }16x2−1211​

Write the form of the partial fraction decomposition of the rational expression.​ 5x−1x2(x−7)\frac { 5 x - 1 } { x ^ { 2 } ( x - 7 ) }x2(x−7)5x−1​ ​

Write the form of the partial fraction decomposition of the rational expression.Do not solve for the constants.​ x+2x2(3x−8)2\frac { x + 2 } { x ^ { 2 } ( 3 x - 8 ) ^ { 2 } }x2(3x−8)2x+2​ ​

Write the form of the partial fraction decomposition of the rational expression.​ 6x−1x(x2−16)\frac { 6 x - 1 } { x \left( x ^ { 2 } - 16 \right) }x(x2−16)6x−1​ ​

Write the form of the partial fraction decomposition of the rational expression.Do not solve for the constants. 1x2+2x\frac { 1 } { x ^ { 2 } + 2 x }x2+2x1​

Write the partial fraction decomposition of the rational expression.​ 3x2+3x+18(x2+6)2\frac { 3 x ^ { 2 } + 3 x + 18 } { \left( x ^ { 2 } + 6 \right) ^ { 2 } }(x2+6)23x2+3x+18​ ​

Write the partial fraction decomposition of the rational expression.Check your result algebraically.​ 5x2+5x\frac { 5 } { x ^ { 2 } + 5 x }x2+5x5​ ​

Write the partial fraction decomposition of the rational expression.Check your result algebraically.​ 2x(x−2)2\frac { 2 x } { ( x - 2 ) ^ { 2 } }(x−2)22x​ ​

Write the partial fraction decomposition of the rational expression.Check your result algebraically.​ 125x2−36\frac { 1 } { 25 x ^ { 2 } - 36 }25x2−361​ ​

Write the partial fraction decomposition of the rational expression.Check your result algebraically.​ 4x2+3x+20(x2+5)2\frac { 4 x ^ { 2 } + 3 x + 20 } { \left( x ^ { 2 } + 5 \right) ^ { 2 } }(x2+5)24x2+3x+20​ ​

Write the form of the partial fraction decomposition of the rational expression.Do not solve for the constants.​ x−36x3+24x\frac { x - 3 } { 6 x ^ { 3 } + 24 x }6x3+24xx−3​ ​

Write the form of the partial fraction decomposition of the rational expression.Do not solve for the constants.​ x−3x2+7x+12\frac { x - 3 } { x ^ { 2 } + 7 x + 12 }x2+7x+12x−3​ ​

Write the partial fraction decomposition of the rational expression.Check your result algebraically.​ 5x2+3x−1x2(x+1)\frac { 5 x ^ { 2 } + 3 x - 1 } { x ^ { 2 } ( x + 1 ) }x2(x+1)5x2+3x−1​ ​

Write the form of the partial fraction decomposition of the rational expression.Do not solve for the constants.​ 4x2−3x\frac { 4 } { x ^ { 2 } - 3 x }x2−3x4​ ​

Rectangular Coordinates

Graphs of Equations

Linear Equations in Two Variables

Functions

Analyzing Graphs of Functions

A Library of Parent Functions

Transformations of Functions

Combinations of Functions Composite Functions

Inverse Functions

Mathematical Modeling and Variation

Quadratic Functions and Models

Polynomial Functions of Higher Degree

Polynomial and Synthetic Division

Complex Numbers

Zeros of Polynomial Functions

Rational Functions

Nonlinear Inequalities

Exponential Functions and Their Graphs

Logarithmic Functions and Their Graphs

Properties of Logarithms

Exponential and Logarithmic Equations

Exponential and Logarithmic Models

Radian and Degree Measure

Trigonometric Functions The Unit Circle

Right Triangle Trigonometry

Trigonometric Functions of Any Angle

Graphs of Sine and Cosine Functions

Graphs of Other Trigonometric Functions

Inverse Trigonometric Functions

Applications and Models

Using Fundamental Identities

Verifying Trigonometric Equations

Solving Trigonometric Equations

Sum and Difference Formulas

Multiple Angle and Product to Sum Formulas

Law of Sines

Law of Cosines

Vectors in the Plane

Vectors and Dot Products

Trigonometric Form of a Complex Number

Linear and Nonlinear Systems of Equations

Two Variable Linear Systems

Multivariable Linear Systems

Systems of Inequalities

Linear Programming

Matrices and Systems of Equations

Operations With Matrices

The Inverse of a Square Matrix

The Determinant of a Square Matrix

Applications of Matrices and Determinants

Sequences and Series

Arithmetic Sequences and Partial Sums

Geometric Sequences and Series

Mathematical Induction

The Binomial Theorem

Counting Principles

Probability

Lines

Introduction to Conics Parabolas

Ellipses

Hyperbolas

Write the form of the partial fraction decomposition of the rational expression.Do not solve for the constants. $\frac { 5 } { x ^ { 3 } - 2 x ^ { 2 } }$

Write the form of the partial fraction decomposition of the rational expression.Do not solve for the constants. $\frac { 5 x + 4 } { ( x + 2 ) ^ { 4 } }$

Write the form of the partial fraction decomposition of the rational expression.Do not solve for the constants. $\frac { x + 5 } { x \left( x ^ { 2 } + 6 \right) ^ { 2 } }$

Write the partial fraction decomposition of the rational expression. $\frac { 5 - x } { 2 x ^ { 2 } + x - 1 }$

Write the partial fraction decomposition of the rational expression. $\frac { 1 } { 16 x ^ { 2 } - 121 }$

Write the form of the partial fraction decomposition of the rational expression. $\frac { 5 x - 1 } { x ^ { 2 } ( x - 7 ) }$

Write the form of the partial fraction decomposition of the rational expression.Do not solve for the constants. $\frac { x + 2 } { x ^ { 2 } ( 3 x - 8 ) ^ { 2 } }$

Write the form of the partial fraction decomposition of the rational expression. $\frac { 6 x - 1 } { x \left( x ^ { 2 } - 16 \right) }$

Write the form of the partial fraction decomposition of the rational expression.Do not solve for the constants. $\frac { 1 } { x ^ { 2 } + 2 x }$

Write the partial fraction decomposition of the rational expression. $\frac { 3 x ^ { 2 } + 3 x + 18 } { \left( x ^ { 2 } + 6 \right) ^ { 2 } }$

Write the partial fraction decomposition of the rational expression.Check your result algebraically. $\frac { 5 } { x ^ { 2 } + 5 x }$

Write the partial fraction decomposition of the rational expression.Check your result algebraically. $\frac { 2 x } { ( x - 2 ) ^ { 2 } }$

Write the partial fraction decomposition of the rational expression.Check your result algebraically. $\frac { 1 } { 25 x ^ { 2 } - 36 }$

Write the partial fraction decomposition of the rational expression.Check your result algebraically. $\frac { 4 x ^ { 2 } + 3 x + 20 } { \left( x ^ { 2 } + 5 \right) ^ { 2 } }$

Write the form of the partial fraction decomposition of the rational expression.Do not solve for the constants. $\frac { x - 3 } { 6 x ^ { 3 } + 24 x }$

Write the form of the partial fraction decomposition of the rational expression.Do not solve for the constants. $\frac { x - 3 } { x ^ { 2 } + 7 x + 12 }$

Write the partial fraction decomposition of the rational expression.Check your result algebraically. $\frac { 5 x ^ { 2 } + 3 x - 1 } { x ^ { 2 } ( x + 1 ) }$

Write the form of the partial fraction decomposition of the rational expression.Do not solve for the constants. $\frac { 4 } { x ^ { 2 } - 3 x }$