Question 1

Simplify the rational expression. If the rational expression cannot be simplified, so state.
-$$\frac { 21 x - 15 } { 5 - 7 x }$$

Accepted Answer

A)  cannot be simplified 
B)  3 
C)  $- 3$ 
D)  $- \frac { 1 } { 3 }$ 
A)  cannot be simplified 
B)  3 
C)  $- 3$ 
D)  $- \frac { 1 } { 3 }$

Question 2

Find all values that make the rational expression undefined. If the rational expression is defined for all real numbers, so
state.
-$$\frac { x ^ { 3 } + 5 x ^ { 4 } } { x ^ { 2 } + 36 }$$

Accepted Answer

A)  $x = - 36$ 
B)  $x = 0 , x = - \frac { 1 } { 5 }$ 
C)  $x = - 6$ 
D)  Defined for all real numbers 
A)  $x = - 36$ 
B)  $x = 0 , x = - \frac { 1 } { 5 }$ 
C)  $x = - 6$ 
D)  Defined for all real numbers

Question 3

Perform the indicated operation(s). Simplify if possible.
-7x x -+ 16 2 - 3x x +- 2 9

Accepted Answer

A)  4x x ++ 25 2 
B)  4x x -+ 25 2 
C)  4x x ++ 2 7 
D)  4x x +- 2 7 
A)  4x x ++ 25 2 
B)  4x x -+ 25 2 
C)  4x x ++ 2 7 
D)  4x x +- 2 7

Question 4

Find the least common denominator of the rational expressions.
-8 and 10 x2 - 25 x( x - 5)

Accepted Answer

A)  x( x + 5)( x - 5) 
B)  ( x2 + 5)( x2 - 5) 
C)  x( x - 5) 
D)  x( x + 5)( x - 5)2 
A)  x( x + 5)( x - 5) 
B)  ( x2 + 5)( x2 - 5) 
C)  x( x - 5) 
D)  x( x + 5)( x - 5)2

Question 5

Divide. Simplify if possible.
-$\frac { 24 x ^ { 4 } } { x ^ { 2 } - 1 } \div \frac { x ^ { 6 } } { ( x + 1 ) ^ { 2 } }$

Accepted Answer

A)  $\frac { 24 x ^ { 24 } } { ( x - 1 ) ( x + 1 ) ^ { 3 } }$ 
B)  $\frac { 4 ( x + 1 ) } { x ^ { 2 } ( x - 1 ) }$ 
C)  $\frac { 24 ( x + 1 ) } { x ^ { 2 } ( x - 1 ) }$ 
D)  $\frac { 24 x ^ { 2 } ( x + 1 ) } { ( x - 1 ) }$ 
A)  $\frac { 24 x ^ { 24 } } { ( x - 1 ) ( x + 1 ) ^ { 3 } }$ 
B)  $\frac { 4 ( x + 1 ) } { x ^ { 2 } ( x - 1 ) }$ 
C)  $\frac { 24 ( x + 1 ) } { x ^ { 2 } ( x - 1 ) }$ 
D)  $\frac { 24 x ^ { 2 } ( x + 1 ) } { ( x - 1 ) }$

Question 6

Simplify the rational expression. If the rational expression cannot be simplified, so state.
-$\frac { ( x - 6 ) ^ { 2 } } { x ^ { 2 } - 36 }$

Accepted Answer

A)  $\frac { x - 6 } { x + 6 }$ 
B)  $\frac { x + 6 } { x - 6 }$ 
C)  cannot be simplified 
D)  1 
A)  $\frac { x - 6 } { x + 6 }$ 
B)  $\frac { x + 6 } { x - 6 }$ 
C)  cannot be simplified 
D)  1

Question 7

Multiply. Simplify if possible.
-$\frac { 3 z ^ { 3 } } { 5 } \cdot \frac { 10 } { z ^ { 2 } }$

Accepted Answer

A)  $\frac { z } { 6 }$ 
B)  $\frac { 6 z ^ { 2 } } { z ^ { 3 } }$ 
C)  $6 z$ 
D)  $\frac { 6 } { \mathrm { z } }$ 
A)  $\frac { z } { 6 }$ 
B)  $\frac { 6 z ^ { 2 } } { z ^ { 3 } }$ 
C)  $6 z$ 
D)  $\frac { 6 } { \mathrm { z } }$

Question 8

Add or subtract as indicated. Simplify the result, if possible.
-$$\frac { x } { x ^ { 2 } - 16 } - \frac { 4 } { 16 - x ^ { 2 } }$$

Accepted Answer

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

Question 9

Simplify the rational expression. If the rational expression cannot be simplified, so state.
-$$\frac { 6 - x } { x - 6 }$$

Accepted Answer

A)  cannot be simplified 
B)  1 
C)  $- 1$ 
D)  $- \mathrm { m }$ 
A)  cannot be simplified 
B)  1 
C)  $- 1$ 
D)  $- \mathrm { m }$

Question 10

Divide. Simplify if possible.
-$$( x + 2 ) \div \frac { x ^ { 2 } - 5 x + 6 } { 3 - x }$$

Accepted Answer

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

Question 11

Divide. Simplify if possible.
-$$\frac { x ^ { 2 } - 12 x + 27 } { 3 - x } \div ( x + 9 )$$

Accepted Answer

A)  $- 1$ 
B)  $- \frac { x - 9 } { x + 9 }$ 
C)  $- ( x - 9 ) ( x + 9 )$ 
D)  $- \frac { x + 9 } { x - 9 }$ 
A)  $- 1$ 
B)  $- \frac { x - 9 } { x + 9 }$ 
C)  $- ( x - 9 ) ( x + 9 )$ 
D)  $- \frac { x + 9 } { x - 9 }$

Question 12

Simplify the rational expression. If the rational expression cannot be simplified, so state.
-$$\frac { x ^ { 3 } - x ^ { 2 } + 3 x - 3 } { x - 1 }$$

Accepted Answer

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

Question 13

Find the least common denominator of the rational expressions.
-$\frac { 7 } { 4 x ^ { 2 } - 8 x + 4 }$ and $\frac { 1 } { 8 x ^ { 2 } - 8 }$

Accepted Answer

A)  $32 ( x - 1 ) ^ { 2 } ( x + 1 )$ 
B)  $4 ( x - 1 ) ^ { 2 } ( x + 1 )$ 
C)  $8 ( x - 1 ) ^ { 2 } ( x + 1 )$ 
D)  $8 ( x - 1 ) ( x + 1 )$ 
A)  $32 ( x - 1 ) ^ { 2 } ( x + 1 )$ 
B)  $4 ( x - 1 ) ^ { 2 } ( x + 1 )$ 
C)  $8 ( x - 1 ) ^ { 2 } ( x + 1 )$ 
D)  $8 ( x - 1 ) ( x + 1 )$

Question 14

Provide an appropriate response.
-The rational expression $$\frac { 120 x } { 100 - x }$$ describes the cost, in millions of dollars, to inoculate x percent of the current population of cattle against a particular virus. Choose which of the following statements are true with regard to this mathematical
Model.
I. The expression will be undefined when x = 100.
II. The cost of inoculating 80 percent of cattle is 200 million dollars more than the cost of inoculating 70 percent of
Cattle.
III. This expression will calculate inoculation costs for any population of cattle, no matter what the size.

Accepted Answer

A)  Only I and III are true. 
B)  All three statements are true. 
C)  Only I and II are true. 
D)  Only II and III are true. 
A)  Only I and III are true. 
B)  All three statements are true. 
C)  Only I and II are true. 
D)  Only II and III are true.

Question 15

Multiply. Simplify if possible.
-$\frac { 2 x ^ { 2 } } { 3 } \cdot \frac { 21 } { x ^ { 3 } }$

Accepted Answer

A)  $\frac { 14 } { x }$ 
B)  $\frac { 14 x ^ { 2 } } { x ^ { 3 } }$ 
C)  $\frac { x } { 14 }$ 
D)  $\frac { 42 x ^ { 2 } } { 3 x ^ { 3 } }$ 
A)  $\frac { 14 } { x }$ 
B)  $\frac { 14 x ^ { 2 } } { x ^ { 3 } }$ 
C)  $\frac { x } { 14 }$ 
D)  $\frac { 42 x ^ { 2 } } { 3 x ^ { 3 } }$

Question 16

Add or subtract as indicated. Simplify the result, if possible.
-$$\frac { x ^ { 2 } + 63 } { x ^ { 2 } + 5 x - 14 } + \frac { 7 - 15 x } { 14 - 5 x - x ^ { 2 } }$$

Accepted Answer

A)  $\frac { ( x - 7 ) ( x - 8 ) } { ( x + 7 ) ( x - 2 ) }$ 
B)  $\frac { x + 8 } { x ^ { 2 } + 5 x - 14 }$ 
C)  $\frac { x + 8 } { x - 2 }$ 
D)  $\frac { x + 7 } { x - 2 }$ 
A)  $\frac { ( x - 7 ) ( x - 8 ) } { ( x + 7 ) ( x - 2 ) }$ 
B)  $\frac { x + 8 } { x ^ { 2 } + 5 x - 14 }$ 
C)  $\frac { x + 8 } { x - 2 }$ 
D)  $\frac { x + 7 } { x - 2 }$

Question 17

Find all values that make the rational expression undefined. If the rational expression is defined for all real numbers, so
state.
-$$\frac { 4 } { r - 4 }$$

Accepted Answer

A)  $\mathrm { r } = 4$ 
B)  $r = 0$ 
C)  $r = - 4$ 
D)  Defined for all real numbers 
A)  $\mathrm { r } = 4$ 
B)  $r = 0$ 
C)  $r = - 4$ 
D)  Defined for all real numbers

Question 18

Simplify the rational expression. If the rational expression cannot be simplified, so state.
-$$\frac { x ^ { 2 } - 16 } { x ^ { 2 } + 8 x + 16 }$$

Accepted Answer

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

Question 19

Simplify the rational expression. If the rational expression cannot be simplified, so state.
-$\frac { x - 5 } { x ^ { 2 } - 25 }$

Accepted Answer

A)  $\frac { 1 } { x + 5 }$ 
B)  $x + 5$ 
C)  $\frac { 1 } { x - 5 }$ 
D)  cannot be simplified 
A)  $\frac { 1 } { x + 5 }$ 
B)  $x + 5$ 
C)  $\frac { 1 } { x - 5 }$ 
D)  cannot be simplified

Question 20

Simplify the rational expression. If the rational expression cannot be simplified, so state.
-$$\frac { 4 x - 8 } { x ^ { 2 } - 5 x + 6 }$$

Accepted Answer

A)  $\frac { 4 } { x + 3 }$ 
B)  cannot be simplified 
C)  $\frac { 4 ( x - 8 ) } { x + 3 }$ 
D)  $\frac { 4 } { x - 3 }$ 
A)  $\frac { 4 } { x + 3 }$ 
B)  cannot be simplified 
C)  $\frac { 4 ( x - 8 ) } { x + 3 }$ 
D)  $\frac { 4 } { x - 3 }$

Simplify the rational expression. If the rational expression cannot be simplified, so state. - $\frac { 21 x - 15 } { 5 - 7 x }$

Find all values that make the rational expression undefined. If the rational expression is defined for all real numbers, so state. - $\frac { x ^ { 3 } + 5 x ^ { 4 } } { x ^ { 2 } + 36 }$

Perform the indicated operation(s). Simplify if possible. -7x x -+ 16 2 - 3x x +- 2 9

Find the least common denominator of the rational expressions. -8 and 10 x² - 25 x( x - 5)

Divide. Simplify if possible. - $\frac { 24 x ^ { 4 } } { x ^ { 2 } - 1 } \div \frac { x ^ { 6 } } { ( x + 1 ) ^ { 2 } }$

Simplify the rational expression. If the rational expression cannot be simplified, so state. - $\frac { ( x - 6 ) ^ { 2 } } { x ^ { 2 } - 36 }$

Multiply. Simplify if possible. - $\frac { 3 z ^ { 3 } } { 5 } \cdot \frac { 10 } { z ^ { 2 } }$

Add or subtract as indicated. Simplify the result, if possible. - $\frac { x } { x ^ { 2 } - 16 } - \frac { 4 } { 16 - x ^ { 2 } }$

Simplify the rational expression. If the rational expression cannot be simplified, so state. - $\frac { 6 - x } { x - 6 }$

Divide. Simplify if possible. - $( x + 2 ) \div \frac { x ^ { 2 } - 5 x + 6 } { 3 - x }$

Divide. Simplify if possible. - $\frac { x ^ { 2 } - 12 x + 27 } { 3 - x } \div ( x + 9 )$

Simplify the rational expression. If the rational expression cannot be simplified, so state. - $\frac { x ^ { 3 } - x ^ { 2 } + 3 x - 3 } { x - 1 }$

Find the least common denominator of the rational expressions. - $\frac { 7 } { 4 x ^ { 2 } - 8 x + 4 }$ and $\frac { 1 } { 8 x ^ { 2 } - 8 }$

Multiply. Simplify if possible. - $\frac { 2 x ^ { 2 } } { 3 } \cdot \frac { 21 } { x ^ { 3 } }$

Add or subtract as indicated. Simplify the result, if possible. - $\frac { x ^ { 2 } + 63 } { x ^ { 2 } + 5 x - 14 } + \frac { 7 - 15 x } { 14 - 5 x - x ^ { 2 } }$

Find all values that make the rational expression undefined. If the rational expression is defined for all real numbers, so state. - $\frac { 4 } { r - 4 }$

Simplify the rational expression. If the rational expression cannot be simplified, so state. - $\frac { x ^ { 2 } - 16 } { x ^ { 2 } + 8 x + 16 }$

Simplify the rational expression. If the rational expression cannot be simplified, so state. - $\frac { x - 5 } { x ^ { 2 } - 25 }$

Simplify the rational expression. If the rational expression cannot be simplified, so state. - $\frac { 4 x - 8 } { x ^ { 2 } - 5 x + 6 }$

Variables, Real Numbers, and Mathematical Models

Linear Equations and Inequalities in One Variable

Linear Equations in Two Variables

Systems of Linear Equations

Exponents and Polynomials

Factoring Polynomials

Basics of Functions

Inequalities and Problem Solving

Radicals, Radical Functions, and Rational Exponents

Filters

Exam 7: Rational Expressions

Simplify the rational expression. If the rational expression cannot be simplified, so state. - 21x−155−7x\frac { 21 x - 15 } { 5 - 7 x }5−7x21x−15​

Find all values that make the rational expression undefined. If the rational expression is defined for all real numbers, so state. - x3+5x4x2+36\frac { x ^ { 3 } + 5 x ^ { 4 } } { x ^ { 2 } + 36 }x2+36x3+5x4​

Perform the indicated operation(s). Simplify if possible. -7x x -+ 16 2 - 3x x +- 2 9

Find the least common denominator of the rational expressions. -8 and 10 x2 - 25 x( x - 5)

Divide. Simplify if possible. - 24x4x2−1÷x6(x+1)2\frac { 24 x ^ { 4 } } { x ^ { 2 } - 1 } \div \frac { x ^ { 6 } } { ( x + 1 ) ^ { 2 } }x2−124x4​÷(x+1)2x6​

Simplify the rational expression. If the rational expression cannot be simplified, so state. - (x−6)2x2−36\frac { ( x - 6 ) ^ { 2 } } { x ^ { 2 } - 36 }x2−36(x−6)2​

Multiply. Simplify if possible. - 3z35⋅10z2\frac { 3 z ^ { 3 } } { 5 } \cdot \frac { 10 } { z ^ { 2 } }53z3​⋅z210​

Add or subtract as indicated. Simplify the result, if possible. - xx2−16−416−x2\frac { x } { x ^ { 2 } - 16 } - \frac { 4 } { 16 - x ^ { 2 } }x2−16x​−16−x24​

Simplify the rational expression. If the rational expression cannot be simplified, so state. - 6−xx−6\frac { 6 - x } { x - 6 }x−66−x​

Divide. Simplify if possible. - (x+2)÷x2−5x+63−x( x + 2 ) \div \frac { x ^ { 2 } - 5 x + 6 } { 3 - x }(x+2)÷3−xx2−5x+6​

Divide. Simplify if possible. - x2−12x+273−x÷(x+9)\frac { x ^ { 2 } - 12 x + 27 } { 3 - x } \div ( x + 9 )3−xx2−12x+27​÷(x+9)

Simplify the rational expression. If the rational expression cannot be simplified, so state. - x3−x2+3x−3x−1\frac { x ^ { 3 } - x ^ { 2 } + 3 x - 3 } { x - 1 }x−1x3−x2+3x−3​

Find the least common denominator of the rational expressions. - 74x2−8x+4\frac { 7 } { 4 x ^ { 2 } - 8 x + 4 }4x2−8x+47​ and 18x2−8\frac { 1 } { 8 x ^ { 2 } - 8 }8x2−81​

Multiply. Simplify if possible. - 2x23⋅21x3\frac { 2 x ^ { 2 } } { 3 } \cdot \frac { 21 } { x ^ { 3 } }32x2​⋅x321​

Add or subtract as indicated. Simplify the result, if possible. - x2+63x2+5x−14+7−15x14−5x−x2\frac { x ^ { 2 } + 63 } { x ^ { 2 } + 5 x - 14 } + \frac { 7 - 15 x } { 14 - 5 x - x ^ { 2 } }x2+5x−14x2+63​+14−5x−x27−15x​

Find all values that make the rational expression undefined. If the rational expression is defined for all real numbers, so state. - 4r−4\frac { 4 } { r - 4 }r−44​

Simplify the rational expression. If the rational expression cannot be simplified, so state. - x2−16x2+8x+16\frac { x ^ { 2 } - 16 } { x ^ { 2 } + 8 x + 16 }x2+8x+16x2−16​

Simplify the rational expression. If the rational expression cannot be simplified, so state. - x−5x2−25\frac { x - 5 } { x ^ { 2 } - 25 }x2−25x−5​

Simplify the rational expression. If the rational expression cannot be simplified, so state. - 4x−8x2−5x+6\frac { 4 x - 8 } { x ^ { 2 } - 5 x + 6 }x2−5x+64x−8​