Question 1

Add or subtract as indicated. Simplify the result, if possible.
-$$\frac { 5 } { x - 7 } + \frac { 4 } { 7 - x }$$

Accepted Answer

A)  $- \frac { 1 } { x - 7 }$ 
B)  $\frac { 1 } { x - 7 }$ 
C)  $\frac { 9 } { x - 7 }$ 
D)  $- \frac { 1 } { 7 - x }$ 
A)  $- \frac { 1 } { x - 7 }$ 
B)  $\frac { 1 } { x - 7 }$ 
C)  $\frac { 9 } { x - 7 }$ 
D)  $- \frac { 1 } { 7 - x }$ B

Question 2

Find all values that make the rational expression undefined. If the rational expression is defined for all real numbers, so
state.
-$$\frac { a - 3 } { 7 - a }$$

Accepted Answer

A)  $a = 7 , a = 3$ 
B)  $a = 7$ 
C)  $a = - 7$ 
D)  Defined for all real numbers 
A)  $a = 7 , a = 3$ 
B)  $a = 7$ 
C)  $a = - 7$ 
D)  Defined for all real numbers B

Question 3

Provide an appropriate response.
-A gas law in chemistry says that $$\frac { \mathrm { PV } } { \mathrm { T } } = \frac { \mathrm { pv } } { \mathrm { t } } . \text { If } \mathrm { T } = 290 , \mathrm { t } = 380 , \mathrm {~V} = 10 , \mathrm { P } = 90 , \text { and } \mathrm { v } = 8$$ , find the value of p. Round to the nearest thousandth.

Accepted Answer

A)  14.741 
B)  147.414 
C)  1012.5 
D)  0.388 
A)  14.741 
B)  147.414 
C)  1012.5 
D)  0.388 B

Question 4

Find the least common denominator of the rational expressions.
-$\frac { 8 } { 15 ( x - 2 ) }$ and $\frac { 7 } { x }$

Accepted Answer

A)  $15 x ^ { 2 } - 2$ 
B)  $15 \left( x ^ { 2 } - 2 \right)$ 
C)  $15 x ( x - 2 )$ 
D)  $15 x - 2$ 
A)  $15 x ^ { 2 } - 2$ 
B)  $15 \left( x ^ { 2 } - 2 \right)$ 
C)  $15 x ( x - 2 )$ 
D)  $15 x - 2$

Question 5

Find the missing expression.
-$$\frac { 11 x + 5 } { x - 1 } + \frac { ? } { x - 1 } = \frac { 14 x + 1 } { x - 1 }$$

Accepted Answer

A)  $3 x + 4$ 
B)  $25 x - 4$ 
C)  $3 x - 4$ 
D)  $25 x - 6$ 
A)  $3 x + 4$ 
B)  $25 x - 4$ 
C)  $3 x - 4$ 
D)  $25 x - 6$

Question 6

Multiply. Simplify if possible.
-$$\frac { w ^ { 2 } - s ^ { 2 } } { w + s } \cdot \frac { w } { w ^ { 2 } - w s }$$

Accepted Answer

A)  1 
B)  $w$ 
C)  $- \frac { 1 } { w }$ 
D)  $- W$ 
A)  1 
B)  $w$ 
C)  $- \frac { 1 } { w }$ 
D)  $- W$

Question 7

Find the least common denominator of the rational expressions.
-$\frac { 4 } { x ^ { 2 } - 36 }$ and $\frac { 8 } { x - 6 }$

Accepted Answer

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

Question 8

Simplify the rational expression. If the rational expression cannot be simplified, so state.
-$\frac { x + 3 } { x ^ { 2 } + 9 }$

Accepted Answer

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

Question 9

Perform the indicated operations. Simplify if possible.
-$$\left( \frac { 9 x ^ { 2 } + 50 x - 24 } { 8 x - 16 } \cdot \frac { x ^ { 2 } - 2 x } { 81 x ^ { 2 } - 16 } \right) \div \frac { 6 x + 36 } { 7 x ^ { 3 } }$$

Accepted Answer

A)  $\frac { 7 x ^ { 4 } } { 48 ( 9 x + 4 ) }$ 
B)  $\frac { 48 } { 7 x ^ { 4 } ( 9 x + 4 ) }$ 
C)  $\frac { 6 ( x + 6 ) ^ { 2 } } { 56 x ^ { 2 } ( 9 x + 4 ) }$ 
D)  $\frac { 7 x ^ { 3 } } { 48 ( 9 x + 4 ) }$ 
A)  $\frac { 7 x ^ { 4 } } { 48 ( 9 x + 4 ) }$ 
B)  $\frac { 48 } { 7 x ^ { 4 } ( 9 x + 4 ) }$ 
C)  $\frac { 6 ( x + 6 ) ^ { 2 } } { 56 x ^ { 2 } ( 9 x + 4 ) }$ 
D)  $\frac { 7 x ^ { 3 } } { 48 ( 9 x + 4 ) }$

Question 10

Perform the indicated operation. Simplify if possible.
-$$\frac { 7 } { 13 + x } + \frac { x + 4 } { 13 + x }$$

Accepted Answer

A)  $\frac { 11 } { 26 }$ 
B)  $\frac { x + 11 } { 13 + x }$ 
C)  $\frac { 11 } { 13 }$ 
D)  $\frac { x + 11 } { 26 + x }$ 
A)  $\frac { 11 } { 26 }$ 
B)  $\frac { x + 11 } { 13 + x }$ 
C)  $\frac { 11 } { 13 }$ 
D)  $\frac { x + 11 } { 26 + x }$

Question 11

Simplify the rational expression. If the rational expression cannot be simplified, so state.
-$$\frac { y ^ { 2 } + 7 y + 10 } { y ^ { 2 } + 10 y + 25 }$$

Accepted Answer

A)  cannot be simplified 
B)  $\frac { 7 y + 2 } { 10 y + 5 }$ 
C)  $\frac { y + 2 } { y + 5 }$ 
D)  $\frac { 7 y + 10 } { 10 y + 25 }$ 
A)  cannot be simplified 
B)  $\frac { 7 y + 2 } { 10 y + 5 }$ 
C)  $\frac { y + 2 } { y + 5 }$ 
D)  $\frac { 7 y + 10 } { 10 y + 25 }$

Question 12

Divide. Simplify if possible.
-$$\frac { 12 x - 12 } { 5 } \div \frac { 4 x - 4 } { 35 }$$

Accepted Answer

A)  $\frac { 48 ( x - 1 ) ^ { 2 } } { 175 }$ 
B)  21 
C)  $\frac { 1 } { 21 }$ 
D)  $\frac { 7 ( 12 x - 12 ) } { 4 x - 4 }$ 
A)  $\frac { 48 ( x - 1 ) ^ { 2 } } { 175 }$ 
B)  21 
C)  $\frac { 1 } { 21 }$ 
D)  $\frac { 7 ( 12 x - 12 ) } { 4 x - 4 }$

Question 13

Perform the indicated operation. Simplify if possible.
-$$\frac { 3 x } { 13 } + \frac { 8 x } { 13 }$$

Accepted Answer

A)  $\frac { 13 x } { 11 }$ 
B)  $\frac { 11 x ^ { 2 } } { 13 }$ 
C)  $\frac { 11 \mathrm { x } } { 26 }$ 
D)  $\frac { 11 \mathrm { x } } { 13 }$ 
A)  $\frac { 13 x } { 11 }$ 
B)  $\frac { 11 x ^ { 2 } } { 13 }$ 
C)  $\frac { 11 \mathrm { x } } { 26 }$ 
D)  $\frac { 11 \mathrm { x } } { 13 }$

Question 14

Find all values that make the rational expression undefined. If the rational expression is defined for all real numbers, so
state.
-$$\frac { 6 y - 4 } { y ^ { 2 } - 9 }$$

Accepted Answer

A)  $y = \frac { 2 } { 3 }$ 
B)  $y = 9$ 
C)  $y = 3 , y = - 3$ 
D)  $y = 3$ 
A)  $y = \frac { 2 } { 3 }$ 
B)  $y = 9$ 
C)  $y = 3 , y = - 3$ 
D)  $y = 3$

Question 15

Find all values that make the rational expression undefined. If the rational expression is defined for all real numbers, so
state.
-$$\frac { x + 2 } { ( x + 7 ) ( x - 3 ) }$$

Accepted Answer

A)  $x = - 2$ 
B)  $x = - 7 , x = 3$ 
C)  $x = - 2 , x = - 7 , x = 3$ 
D)  Defined for all real numbers 
A)  $x = - 2$ 
B)  $x = - 7 , x = 3$ 
C)  $x = - 2 , x = - 7 , x = 3$ 
D)  Defined for all real numbers

Question 16

Perform the indicated operation(s). Simplify if possible.
-$$\frac { 8 y ^ { 2 } } { y - 1 } - \frac { 8 y } { y - 1 }$$

Accepted Answer

A)  $\frac { 8 y } { y - 1 }$ 
B)  0 
C)  $8 \mathrm { y }$ 
D)  $\frac { 8 y ( y + 1 ) } { y - 1 }$ 
A)  $\frac { 8 y } { y - 1 }$ 
B)  0 
C)  $8 \mathrm { y }$ 
D)  $\frac { 8 y ( y + 1 ) } { y - 1 }$

Question 17

Perform the indicated operation. Simplify if possible.
-Express the perimeter of the rectangle as a fully simplified rational expression. 10 - 2x inches
X + 2
12x + 10 inches
X + 2

Accepted Answer

A)  100x + 100 in. 
B)  20 in. 
C)  10 in. 
D)  10x in. x2+ 4x + b2 
A)  100x + 100 in. 
B)  20 in. 
C)  10 in. 
D)  10x in. x2+ 4x + b2

Question 18

Find the least common denominator of the rational expressions.
-$\frac { 3 } { x ^ { 2 } + 3 x }$ and $\frac { 9 } { x ^ { 2 } + 9 x + 18 }$

Accepted Answer

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

Question 19

Simplify the rational expression. If the rational expression cannot be simplified, so state.
-$$\frac { 6 x - 18 } { 15 - 5 x }$$

Accepted Answer

A)  $\frac { 6 } { 5 }$ 
B)  $- \frac { 6 } { 5 }$ 
C)  1 
D)  $- 1$ 
A)  $\frac { 6 } { 5 }$ 
B)  $- \frac { 6 } { 5 }$ 
C)  1 
D)  $- 1$

Question 20

Find the least common denominator of the rational expressions.
-$\frac { 4 } { x - 10 }$ and $\frac { 2 } { x + 1 }$

Accepted Answer

A)  8 
B)  $x + 1$ 
C)  $8 ( x - 10 ) ( x + 1 )$ 
D)  $( x - 10 ) ( x + 1 )$ 
A)  8 
B)  $x + 1$ 
C)  $8 ( x - 10 ) ( x + 1 )$ 
D)  $( x - 10 ) ( x + 1 )$

Add or subtract as indicated. Simplify the result, if possible. - $\frac { 5 } { x - 7 } + \frac { 4 } { 7 - x }$

Find all values that make the rational expression undefined. If the rational expression is defined for all real numbers, so state. - $\frac { a - 3 } { 7 - a }$

Find the least common denominator of the rational expressions. - $\frac { 8 } { 15 ( x - 2 ) }$ and $\frac { 7 } { x }$

Find the missing expression. - $\frac { 11 x + 5 } { x - 1 } + \frac { ? } { x - 1 } = \frac { 14 x + 1 } { x - 1 }$

Multiply. Simplify if possible. - $\frac { w ^ { 2 } - s ^ { 2 } } { w + s } \cdot \frac { w } { w ^ { 2 } - w s }$

Find the least common denominator of the rational expressions. - $\frac { 4 } { x ^ { 2 } - 36 }$ and $\frac { 8 } { x - 6 }$

Simplify the rational expression. If the rational expression cannot be simplified, so state. - $\frac { x + 3 } { x ^ { 2 } + 9 }$

Perform the indicated operations. Simplify if possible. - $\left( \frac { 9 x ^ { 2 } + 50 x - 24 } { 8 x - 16 } \cdot \frac { x ^ { 2 } - 2 x } { 81 x ^ { 2 } - 16 } \right) \div \frac { 6 x + 36 } { 7 x ^ { 3 } }$

Perform the indicated operation. Simplify if possible. - $\frac { 7 } { 13 + x } + \frac { x + 4 } { 13 + x }$

Simplify the rational expression. If the rational expression cannot be simplified, so state. - $\frac { y ^ { 2 } + 7 y + 10 } { y ^ { 2 } + 10 y + 25 }$

Divide. Simplify if possible. - $\frac { 12 x - 12 } { 5 } \div \frac { 4 x - 4 } { 35 }$

Perform the indicated operation. Simplify if possible. - $\frac { 3 x } { 13 } + \frac { 8 x } { 13 }$

Find all values that make the rational expression undefined. If the rational expression is defined for all real numbers, so state. - $\frac { 6 y - 4 } { y ^ { 2 } - 9 }$

Find all values that make the rational expression undefined. If the rational expression is defined for all real numbers, so state. - $\frac { x + 2 } { ( x + 7 ) ( x - 3 ) }$

Perform the indicated operation(s). Simplify if possible. - $\frac { 8 y ^ { 2 } } { y - 1 } - \frac { 8 y } { y - 1 }$

Perform the indicated operation. Simplify if possible. -Express the perimeter of the rectangle as a fully simplified rational expression. 10 - 2x inches X + 2 12x + 10 inches X + 2

Find the least common denominator of the rational expressions. - $\frac { 3 } { x ^ { 2 } + 3 x }$ and $\frac { 9 } { x ^ { 2 } + 9 x + 18 }$

Simplify the rational expression. If the rational expression cannot be simplified, so state. - $\frac { 6 x - 18 } { 15 - 5 x }$

Find the least common denominator of the rational expressions. - $\frac { 4 } { x - 10 }$ and $\frac { 2 } { x + 1 }$

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

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Exam 7: Rational Expressions

Add or subtract as indicated. Simplify the result, if possible. - 5x−7+47−x\frac { 5 } { x - 7 } + \frac { 4 } { 7 - x }x−75​+7−x4​

Find all values that make the rational expression undefined. If the rational expression is defined for all real numbers, so state. - a−37−a\frac { a - 3 } { 7 - a }7−aa−3​

Find the least common denominator of the rational expressions. - 815(x−2)\frac { 8 } { 15 ( x - 2 ) }15(x−2)8​ and 7x\frac { 7 } { x }x7​

Find the missing expression. - 11x+5x−1+?x−1=14x+1x−1\frac { 11 x + 5 } { x - 1 } + \frac { ? } { x - 1 } = \frac { 14 x + 1 } { x - 1 }x−111x+5​+x−1?​=x−114x+1​

Multiply. Simplify if possible. - w2−s2w+s⋅ww2−ws\frac { w ^ { 2 } - s ^ { 2 } } { w + s } \cdot \frac { w } { w ^ { 2 } - w s }w+sw2−s2​⋅w2−wsw​

Find the least common denominator of the rational expressions. - 4x2−36\frac { 4 } { x ^ { 2 } - 36 }x2−364​ and 8x−6\frac { 8 } { x - 6 }x−68​

Simplify the rational expression. If the rational expression cannot be simplified, so state. - x+3x2+9\frac { x + 3 } { x ^ { 2 } + 9 }x2+9x+3​

Perform the indicated operation. Simplify if possible. - 713+x+x+413+x\frac { 7 } { 13 + x } + \frac { x + 4 } { 13 + x }13+x7​+13+xx+4​

Simplify the rational expression. If the rational expression cannot be simplified, so state. - y2+7y+10y2+10y+25\frac { y ^ { 2 } + 7 y + 10 } { y ^ { 2 } + 10 y + 25 }y2+10y+25y2+7y+10​

Divide. Simplify if possible. - 12x−125÷4x−435\frac { 12 x - 12 } { 5 } \div \frac { 4 x - 4 } { 35 }512x−12​÷354x−4​

Perform the indicated operation. Simplify if possible. - 3x13+8x13\frac { 3 x } { 13 } + \frac { 8 x } { 13 }133x​+138x​

Find all values that make the rational expression undefined. If the rational expression is defined for all real numbers, so state. - 6y−4y2−9\frac { 6 y - 4 } { y ^ { 2 } - 9 }y2−96y−4​

Find all values that make the rational expression undefined. If the rational expression is defined for all real numbers, so state. - x+2(x+7)(x−3)\frac { x + 2 } { ( x + 7 ) ( x - 3 ) }(x+7)(x−3)x+2​

Perform the indicated operation(s). Simplify if possible. - 8y2y−1−8yy−1\frac { 8 y ^ { 2 } } { y - 1 } - \frac { 8 y } { y - 1 }y−18y2​−y−18y​