Question 1

Write the partial fraction decomposition of the rational expression.Check your result algebraically.​ $~~~~~~~~26$
$\overline { x ^ { 2 } + 3 x - 40 }$ ​

Accepted Answer

A)  $\frac { 1 } { x - 5 } + \frac { 1 } { x + 8 }$ 
B)  $\frac { 1 } { x - 5 } - \frac { 1 } { x + 8 }$ 
C)  $\frac { 2 } { x - 5 } - \frac { 2 } { x + 8 }$ 
D)  $\frac { 2 } { x + 5 } - \frac { 2 } { x - 8 }$ 
E)  $\frac { 2 } { x - 5 } + \frac { 2 } { x + 8 }$ 
A)  $\frac { 1 } { x - 5 } + \frac { 1 } { x + 8 }$ 
B)  $\frac { 1 } { x - 5 } - \frac { 1 } { x + 8 }$ 
C)  $\frac { 2 } { x - 5 } - \frac { 2 } { x + 8 }$ 
D)  $\frac { 2 } { x + 5 } - \frac { 2 } { x - 8 }$ 
E)  $\frac { 2 } { x - 5 } + \frac { 2 } { x + 8 }$

Question 2

Write the partial fraction decomposition of the rational expression.Check your result algebraically.​ $\frac { 3 x ^ { 2 } + 7 x + 7 } { x ^ { 3 } + x }$ ​

Accepted Answer

A)  $\frac { 7 } { x } - \frac { 4 x + 7 } { x ^ { 2 } + 1 }$ 
B)  $\frac { 7 } { x } + \frac { 4 x - 7 } { x ^ { 2 } + 1 }$ 
C)  $\frac { 7 } { x } + \frac { 4 x + 7 } { x ^ { 2 } + 1 }$ 
D)  $\frac { 7 } { x } - \frac { 7 x - 7 } { x ^ { 2 } + 1 }$ 
E)  $\frac { 7 } { x } - \frac { 4 x - 7 } { x ^ { 2 } + 1 }$ 
A)  $\frac { 7 } { x } - \frac { 4 x + 7 } { x ^ { 2 } + 1 }$ 
B)  $\frac { 7 } { x } + \frac { 4 x - 7 } { x ^ { 2 } + 1 }$ 
C)  $\frac { 7 } { x } + \frac { 4 x + 7 } { x ^ { 2 } + 1 }$ 
D)  $\frac { 7 } { x } - \frac { 7 x - 7 } { x ^ { 2 } + 1 }$ 
E)  $\frac { 7 } { x } - \frac { 4 x - 7 } { x ^ { 2 } + 1 }$

Question 3

Write the form of the partial fraction decomposition of the rational expression.Do not solve for the constants.​ $$\frac { 7 x ^ { 2 } + 6 } { ( x - 6 ) ^ { 3 } }$$ ​

Accepted Answer

A)  $\frac { A } { ( x - 6 ) ^ { 3 } }$ 
B)  $\frac { 7 } { x - 6 } + \frac { 6 } { x - 6 } + \frac { 6 } { x - 6 }$ 
C)  $\frac { A } { x - 6 } + \frac { B } { ( x - 6 ) ^ { 2 } }$ 
D)  $\frac { A } { x - 6 } + \frac { B } { ( x - 6 ) ^ { 2 } } + \frac { C } { ( x - 6 ) ^ { 3 } }$ 
E)  $\frac { A } { 6 ( x - 6 ) } - \frac { B } { 7 ( x - 6 ) ^ { 2 } } - \frac { C } { 7 ( x - 6 ) ^ { 3 } }$ 
A)  $\frac { A } { ( x - 6 ) ^ { 3 } }$ 
B)  $\frac { 7 } { x - 6 } + \frac { 6 } { x - 6 } + \frac { 6 } { x - 6 }$ 
C)  $\frac { A } { x - 6 } + \frac { B } { ( x - 6 ) ^ { 2 } }$ 
D)  $\frac { A } { x - 6 } + \frac { B } { ( x - 6 ) ^ { 2 } } + \frac { C } { ( x - 6 ) ^ { 3 } }$ 
E)  $\frac { A } { 6 ( x - 6 ) } - \frac { B } { 7 ( x - 6 ) ^ { 2 } } - \frac { C } { 7 ( x - 6 ) ^ { 3 } }$

Question 4

Write the partial fraction decomposition of the rational expression. $\frac { x ^ { 2 } } { x ^ { 4 } - 23 x ^ { 2 } - 50 }$

Accepted Answer

A) ​ $\frac { 1 } { x ^ { 2 } } - \frac { 1 } { 6 } - \frac { x ^ { 2 } } { 10 }$ 
B)  $\frac { 1 } { 27 } \left( \frac { 2 } { x ^ { 2 } + 2 } + \frac { 5 } { 2 ( x - 5 ) } - \frac { 5 } { 2 ( x + 5 ) } \right)$ 
C)  $\frac { 1 } { 27 } \left( \frac { 2 } { x ^ { 2 } + 2 } + \frac { 5 ( x + 2 ) } { 2 ( x - 5 ) } + \frac { 5 } { 2 ( x - 5 ) } \right)$ 
D)  $\frac { 1 } { 27 } \left( \frac { 2 } { x ^ { 2 } + 2 } - \frac { 5 } { 2 ( x - 5 ) } + \frac { 5 } { 2 ( x + 5 ) } \right)$ 
E)  $\frac { 1 } { 27 } \left( \frac { 2 } { x ^ { 2 } + 2 } + \frac { 5 } { 2 ( x - 5 ) } - \frac { 5 } { 2 ( x + 5 ) } \right)$ 
A) ​ $\frac { 1 } { x ^ { 2 } } - \frac { 1 } { 6 } - \frac { x ^ { 2 } } { 10 }$ 
B)  $\frac { 1 } { 27 } \left( \frac { 2 } { x ^ { 2 } + 2 } + \frac { 5 } { 2 ( x - 5 ) } - \frac { 5 } { 2 ( x + 5 ) } \right)$ 
C)  $\frac { 1 } { 27 } \left( \frac { 2 } { x ^ { 2 } + 2 } + \frac { 5 ( x + 2 ) } { 2 ( x - 5 ) } + \frac { 5 } { 2 ( x - 5 ) } \right)$ 
D)  $\frac { 1 } { 27 } \left( \frac { 2 } { x ^ { 2 } + 2 } - \frac { 5 } { 2 ( x - 5 ) } + \frac { 5 } { 2 ( x + 5 ) } \right)$ 
E)  $\frac { 1 } { 27 } \left( \frac { 2 } { x ^ { 2 } + 2 } + \frac { 5 } { 2 ( x - 5 ) } - \frac { 5 } { 2 ( x + 5 ) } \right)$

Question 5

Write the partial fraction decomposition of the rational expression.Check your result algebraically.​ $\frac { 1 } { 4 x ^ { 2 } + x }$ ​

Accepted Answer

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

Question 6

Write the form of the partial fraction decomposition of the rational expression.​ $$\frac { 6 x - 1 } { x ( x - 4 ) }$$ ​

Accepted Answer

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

Question 7

Write the partial fraction decomposition of the rational expression.​ $\frac { 1 } { ( x + 1 ) ( a - x ) }$ ​

Accepted Answer

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

Question 8

Write the partial fraction decomposition of the rational function.​ $\frac { 2 ( 4 x - 3 ) } { x ^ { 2 } - 9 }$ ​

Accepted Answer

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

Question 9

Write the partial fraction decomposition of the rational expression.Check your result algebraically.​ $\frac { 8 } { x ^ { 2 } + 2 x - 3 }$ ​

Accepted Answer

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

Question 10

Write the partial fraction decomposition of the rational expression.​ $\frac { 1 } { y ( q - y ) }$ ​

Accepted Answer

A)  $\frac { 1 } { q } \left( \frac { 1 } { y } + \frac { 1 } { q + y } \right)$ 
B)  $\frac { 1 } { q } \left( \frac { 1 } { y } - \frac { 1 } { q - y } \right)$ 
C)  $\frac { 1 } { y } + \frac { 1 } { q - y }$ 
D)  $\frac { 1 } { q } \left( \frac { 1 } { y } + \frac { 1 } { q - y } \right)$ 
E)  $\frac { 1 } { q } \left( - \frac { 1 } { y } - \frac { 1 } { q - y } \right)$ 
A)  $\frac { 1 } { q } \left( \frac { 1 } { y } + \frac { 1 } { q + y } \right)$ 
B)  $\frac { 1 } { q } \left( \frac { 1 } { y } - \frac { 1 } { q - y } \right)$ 
C)  $\frac { 1 } { y } + \frac { 1 } { q - y }$ 
D)  $\frac { 1 } { q } \left( \frac { 1 } { y } + \frac { 1 } { q - y } \right)$ 
E)  $\frac { 1 } { q } \left( - \frac { 1 } { y } - \frac { 1 } { q - y } \right)$

Question 11

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

Accepted Answer

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

Question 12

Write the partial fraction decomposition of the rational function.​ $\frac { x - 16 } { x ( x - 4 ) }$ ​

Accepted Answer

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

Question 13

Write the partial fraction decomposition of the rational expression.​ $\frac { 1 } { x ( x + q ) }$ ​

Accepted Answer

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

Question 14

Write the partial fraction decomposition of the rational expression.Check your result algebraically.​ $\frac { 7 x - 8 } { ( x - 1 ) ^ { 2 } }$ ​

Accepted Answer

A)  $\frac { 7 } { x - 1 } + \frac { 1 } { ( x + 1 ) ^ { 3 } }$ 
B)  $\frac { 7 } { x - 1 } - \frac { 1 } { ( x + 1 ) ^ { 2 } }$ 
C)  $\frac { 7 } { ( x - 1 ) ^ { 2 } } - \frac { 1 } { ( x - 1 ) ^ { 3 } }$ 
D)  $\frac { 7 } { x - 1 } - \frac { 1 } { ( x - 1 ) ^ { 2 } }$ 
E)  $\frac { 7 } { x - 1 } + \frac { 1 } { ( x - 1 ) ^ { 2 } }$ 
A)  $\frac { 7 } { x - 1 } + \frac { 1 } { ( x + 1 ) ^ { 3 } }$ 
B)  $\frac { 7 } { x - 1 } - \frac { 1 } { ( x + 1 ) ^ { 2 } }$ 
C)  $\frac { 7 } { ( x - 1 ) ^ { 2 } } - \frac { 1 } { ( x - 1 ) ^ { 3 } }$ 
D)  $\frac { 7 } { x - 1 } - \frac { 1 } { ( x - 1 ) ^ { 2 } }$ 
E)  $\frac { 7 } { x - 1 } + \frac { 1 } { ( x - 1 ) ^ { 2 } }$

Question 15

Write the partial fraction decomposition of the improper rational expression. $\frac { x ^ { 2 } + 4 x } { x ^ { 2 } + x + 1 }$ ​

Accepted Answer

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

Question 16

Write the form of the partial fraction decomposition of the rational expression.Do not solve for the constants.​ $$\frac { x - 4 } { x \left( x ^ { 2 } + 7 \right) ^ { 2 } }$$ ​

Accepted Answer

A)  $\frac { A } { x } + \frac { B } { x ^ { 2 } + 7 } + \frac { C } { \left( x ^ { 2 } + 7 x ^ { 4 } \right) ^ { 2 } }$ ​ 
B)  $\frac { A } { x } + \frac { B x + C } { x ^ { 2 } + 7 } + \frac { D x + E } { ( x + 7 ) ^ { 2 } }$ ​ 
C)  $\frac { A } { x } - \frac { B x + C } { \left( x ^ { 2 } + 7 \right) ^ { 2 } } - \frac { D x + E } { x \left( x ^ { 2 } + 7 \right) ^ { 2 } }$ ​ 
D)  $\frac { A } { x } + \frac { B x + C } { x ^ { 2 } + 7 } + \frac { D x + E } { \left( x ^ { 2 } + 7 \right) ^ { 2 } }$ ​ 
E)  $\frac { A } { x - 4 } + \frac { B x + C } { x ^ { 2 } + 7 } + \frac { D x + E } { \left( x ^ { 2 } + 7 \right) ^ { 2 } }$ 
A)  $\frac { A } { x } + \frac { B } { x ^ { 2 } + 7 } + \frac { C } { \left( x ^ { 2 } + 7 x ^ { 4 } \right) ^ { 2 } }$ ​ 
B)  $\frac { A } { x } + \frac { B x + C } { x ^ { 2 } + 7 } + \frac { D x + E } { ( x + 7 ) ^ { 2 } }$ ​ 
C)  $\frac { A } { x } - \frac { B x + C } { \left( x ^ { 2 } + 7 \right) ^ { 2 } } - \frac { D x + E } { x \left( x ^ { 2 } + 7 \right) ^ { 2 } }$ ​ 
D)  $\frac { A } { x } + \frac { B x + C } { x ^ { 2 } + 7 } + \frac { D x + E } { \left( x ^ { 2 } + 7 \right) ^ { 2 } }$ ​ 
E)  $\frac { A } { x - 4 } + \frac { B x + C } { x ^ { 2 } + 7 } + \frac { D x + E } { \left( x ^ { 2 } + 7 \right) ^ { 2 } }$

Question 17

Write the form of the partial fraction decomposition of the rational expression.Do not solve for the constants. $\frac { 6 x ^ { 2 } - 1 } { ( x + 8 ) ^ { 3 } }$

Accepted Answer

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

Question 18

Write the partial fraction decomposition of the improper rational expression. $\frac { x ^ { 3 } - 2 x ^ { 2 } - 14 x + 48 } { x ^ { 2 } + x - 20 }$

Accepted Answer

A)  $\frac { 1 } { 3 } \left( \frac { 8 } { x - 4 } + \frac { 19 } { x + 5 } \right)$ 
B)  $x - 3 + \frac { 1 } { 3 } \left( \frac { 8 } { x - 4 } - \frac { 19 } { x + 5 } \right)$ 
C) ​ $x - 3 + \frac { 1 } { 3 } \left( \frac { 8 } { x - 4 } + \frac { 19 } { x + 5 } \right)$ 
D)  $x - 3 + \frac { 1 } { 3 } \left( \frac { 16 } { x + 4 } + \frac { 19 } { x - 5 } \right)$ 
E)  $x - 3 - \frac { 1 } { 3 } \left( \frac { 16 } { x - 4 } - \frac { 19 } { x - 5 } \right)$ 
A)  $\frac { 1 } { 3 } \left( \frac { 8 } { x - 4 } + \frac { 19 } { x + 5 } \right)$ 
B)  $x - 3 + \frac { 1 } { 3 } \left( \frac { 8 } { x - 4 } - \frac { 19 } { x + 5 } \right)$ 
C) ​ $x - 3 + \frac { 1 } { 3 } \left( \frac { 8 } { x - 4 } + \frac { 19 } { x + 5 } \right)$ 
D)  $x - 3 + \frac { 1 } { 3 } \left( \frac { 16 } { x + 4 } + \frac { 19 } { x - 5 } \right)$ 
E)  $x - 3 - \frac { 1 } { 3 } \left( \frac { 16 } { x - 4 } - \frac { 19 } { x - 5 } \right)$

Question 19

Write the partial fraction decomposition of the rational expression.Check your result algebraically.​ $\frac { 1 } { x ^ { 2 } - 16 }$ ​

Accepted Answer

A)  $\frac { 1 } { 8 } \left( \frac { A } { x - 4 } - \frac { B } { x + 4 } \right)$ 
B)  $\frac { 8 } { x - 4 } - \frac { 8 } { x + 4 }$ 
C)  $\frac { 1 } { 8 } \left( \frac { 8 } { x - 4 } - \frac { 8 } { x + 4 } \right)$ 
D)  $\frac { 1 } { 8 } \left( \frac { 1 } { x - 4 } - \frac { 1 } { x + 4 } \right)$ 
E)  $\frac { 1 } { 8 } \left( \frac { 1 } { x - 4 } + \frac { 1 } { x + 4 } \right)$ 
A)  $\frac { 1 } { 8 } \left( \frac { A } { x - 4 } - \frac { B } { x + 4 } \right)$ 
B)  $\frac { 8 } { x - 4 } - \frac { 8 } { x + 4 }$ 
C)  $\frac { 1 } { 8 } \left( \frac { 8 } { x - 4 } - \frac { 8 } { x + 4 } \right)$ 
D)  $\frac { 1 } { 8 } \left( \frac { 1 } { x - 4 } - \frac { 1 } { x + 4 } \right)$ 
E)  $\frac { 1 } { 8 } \left( \frac { 1 } { x - 4 } + \frac { 1 } { x + 4 } \right)$

Question 20

​Write the partial fraction decomposition of the rational expression. $\frac { 9 } { x ^ { 2 } + 16 x + 63 }$

Accepted Answer

A) ​ $\frac { 9 } { 2 } \left( \frac { 1 } { x + 9 } - \frac { 1 } { x + 7 } \right)$ 
B) ​ $\frac { 9 } { x ^ { 2 } + 16 x + 63 }$ 
C) ​ $\frac { 9 } { x ^ { 2 } } + \frac { 9 } { 16 x } + \frac { 1 } { 7 }$ 
D) ​ $\frac { 9 } { 2 } \left( \frac { 1 } { x - 7 } - \frac { 1 } { x - 9 } \right)$ 
E)  $\frac { 9 } { 2 } \left( \frac { 1 } { x + 7 } - \frac { 1 } { x + 9 } \right)$ 
A) ​ $\frac { 9 } { 2 } \left( \frac { 1 } { x + 9 } - \frac { 1 } { x + 7 } \right)$ 
B) ​ $\frac { 9 } { x ^ { 2 } + 16 x + 63 }$ 
C) ​ $\frac { 9 } { x ^ { 2 } } + \frac { 9 } { 16 x } + \frac { 1 } { 7 }$ 
D) ​ $\frac { 9 } { 2 } \left( \frac { 1 } { x - 7 } - \frac { 1 } { x - 9 } \right)$ 
E)  $\frac { 9 } { 2 } \left( \frac { 1 } { x + 7 } - \frac { 1 } { x + 9 } \right)$

Exam 44: Partial Fractions

Write the partial fraction decomposition of the rational expression.Check your result algebraically.​ 26~~~~~~~~26 26 x2+3x−40‾\overline { x ^ { 2 } + 3 x - 40 }x2+3x−40​ ​

Write the partial fraction decomposition of the rational expression.Check your result algebraically.​ 3x2+7x+7x3+x\frac { 3 x ^ { 2 } + 7 x + 7 } { x ^ { 3 } + x }x3+x3x2+7x+7​ ​

Write the form of the partial fraction decomposition of the rational expression.Do not solve for the constants.​ 7x2+6(x−6)3\frac { 7 x ^ { 2 } + 6 } { ( x - 6 ) ^ { 3 } }(x−6)37x2+6​ ​

Write the partial fraction decomposition of the rational expression. x2x4−23x2−50\frac { x ^ { 2 } } { x ^ { 4 } - 23 x ^ { 2 } - 50 }x4−23x2−50x2​

Write the partial fraction decomposition of the rational expression.Check your result algebraically.​ 14x2+x\frac { 1 } { 4 x ^ { 2 } + x }4x2+x1​ ​

Write the form of the partial fraction decomposition of the rational expression.​ 6x−1x(x−4)\frac { 6 x - 1 } { x ( x - 4 ) }x(x−4)6x−1​ ​

Write the partial fraction decomposition of the rational expression.​ 1(x+1)(a−x)\frac { 1 } { ( x + 1 ) ( a - x ) }(x+1)(a−x)1​ ​

Write the partial fraction decomposition of the rational function.​ 2(4x−3)x2−9\frac { 2 ( 4 x - 3 ) } { x ^ { 2 } - 9 }x2−92(4x−3)​ ​

Write the partial fraction decomposition of the rational expression.Check your result algebraically.​ 8x2+2x−3\frac { 8 } { x ^ { 2 } + 2 x - 3 }x2+2x−38​ ​

Write the partial fraction decomposition of the rational expression.​ 1y(q−y)\frac { 1 } { y ( q - y ) }y(q−y)1​ ​

Write the partial fraction decomposition of the rational expression.Check your result algebraically.​ 3x2−3x−2x3−x\frac { 3 x ^ { 2 } - 3 x - 2 } { x ^ { 3 } - x }x3−x3x2−3x−2​ ​

Write the partial fraction decomposition of the rational function.​ x−16x(x−4)\frac { x - 16 } { x ( x - 4 ) }x(x−4)x−16​ ​

Write the partial fraction decomposition of the rational expression.​ 1x(x+q)\frac { 1 } { x ( x + q ) }x(x+q)1​ ​

Write the partial fraction decomposition of the rational expression.Check your result algebraically.​ 7x−8(x−1)2\frac { 7 x - 8 } { ( x - 1 ) ^ { 2 } }(x−1)27x−8​ ​

Write the partial fraction decomposition of the improper rational expression. x2+4xx2+x+1\frac { x ^ { 2 } + 4 x } { x ^ { 2 } + x + 1 }x2+x+1x2+4x​ ​

Write the form of the partial fraction decomposition of the rational expression.Do not solve for the constants.​ x−4x(x2+7)2\frac { x - 4 } { x \left( x ^ { 2 } + 7 \right) ^ { 2 } }x(x2+7)2x−4​ ​

Write the form of the partial fraction decomposition of the rational expression.Do not solve for the constants. 6x2−1(x+8)3\frac { 6 x ^ { 2 } - 1 } { ( x + 8 ) ^ { 3 } }(x+8)36x2−1​

Write the partial fraction decomposition of the improper rational expression. x3−2x2−14x+48x2+x−20\frac { x ^ { 3 } - 2 x ^ { 2 } - 14 x + 48 } { x ^ { 2 } + x - 20 }x2+x−20x3−2x2−14x+48​

Write the partial fraction decomposition of the rational expression.Check your result algebraically.​ 1x2−16\frac { 1 } { x ^ { 2 } - 16 }x2−161​ ​

​Write the partial fraction decomposition of the rational expression. 9x2+16x+63\frac { 9 } { x ^ { 2 } + 16 x + 63 }x2+16x+639​

Rectangular Coordinates

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Analyzing Graphs of Functions

A Library of Parent Functions

Transformations of Functions

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Mathematical Modeling and Variation

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Polynomial Functions of Higher Degree

Polynomial and Synthetic Division

Complex Numbers

Zeros of Polynomial Functions

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Nonlinear Inequalities

Exponential Functions and Their Graphs

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Properties of Logarithms

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Linear and Nonlinear Systems of Equations

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The Determinant of a Square Matrix

Applications of Matrices and Determinants

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Mathematical Induction

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Introduction to Conics Parabolas

Write the partial fraction decomposition of the rational expression.Check your result algebraically. $~~~~~~~~26$ $\overline { x ^ { 2 } + 3 x - 40 }$

Write the partial fraction decomposition of the rational expression.Check your result algebraically. $\frac { 3 x ^ { 2 } + 7 x + 7 } { x ^ { 3 } + x }$

Write the form of the partial fraction decomposition of the rational expression.Do not solve for the constants. $\frac { 7 x ^ { 2 } + 6 } { ( x - 6 ) ^ { 3 } }$

Write the partial fraction decomposition of the rational expression. $\frac { x ^ { 2 } } { x ^ { 4 } - 23 x ^ { 2 } - 50 }$

Write the partial fraction decomposition of the rational expression.Check your result algebraically. $\frac { 1 } { 4 x ^ { 2 } + x }$

Write the form of the partial fraction decomposition of the rational expression. $\frac { 6 x - 1 } { x ( x - 4 ) }$

Write the partial fraction decomposition of the rational expression. $\frac { 1 } { ( x + 1 ) ( a - x ) }$

Write the partial fraction decomposition of the rational function. $\frac { 2 ( 4 x - 3 ) } { x ^ { 2 } - 9 }$

Write the partial fraction decomposition of the rational expression.Check your result algebraically. $\frac { 8 } { x ^ { 2 } + 2 x - 3 }$

Write the partial fraction decomposition of the rational expression. $\frac { 1 } { y ( q - y ) }$

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

Write the partial fraction decomposition of the rational function. $\frac { x - 16 } { x ( x - 4 ) }$

Write the partial fraction decomposition of the rational expression. $\frac { 1 } { x ( x + q ) }$

Write the partial fraction decomposition of the rational expression.Check your result algebraically. $\frac { 7 x - 8 } { ( x - 1 ) ^ { 2 } }$

Write the partial fraction decomposition of the improper rational expression. $\frac { x ^ { 2 } + 4 x } { x ^ { 2 } + x + 1 }$

Write the form of the partial fraction decomposition of the rational expression.Do not solve for the constants. $\frac { x - 4 } { x \left( x ^ { 2 } + 7 \right) ^ { 2 } }$

Write the form of the partial fraction decomposition of the rational expression.Do not solve for the constants. $\frac { 6 x ^ { 2 } - 1 } { ( x + 8 ) ^ { 3 } }$

Write the partial fraction decomposition of the improper rational expression. $\frac { x ^ { 3 } - 2 x ^ { 2 } - 14 x + 48 } { x ^ { 2 } + x - 20 }$

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

Write the partial fraction decomposition of the rational expression. $\frac { 9 } { x ^ { 2 } + 16 x + 63 }$