Question 1

Perform the indicated operation. Simplify if possible.
-Express the perimeter of the rectangle as a fully simplified rational expression.

Accepted Answer

A)  $\frac { 100 x + 300 } { x ^ { 2 } + 8 x + 16 }$ in. 
B)  $10 \mathrm { in }$. 
C)  $20 \mathrm { in } .$ 
D)  $10 \mathrm { x }$ in. 
A)  $\frac { 100 x + 300 } { x ^ { 2 } + 8 x + 16 }$ in. 
B)  $10 \mathrm { in }$. 
C)  $20 \mathrm { in } .$ 
D)  $10 \mathrm { x }$ in.

Question 2

Multiply. Simplify if possible.
-$$\frac { k ^ { 2 } + 12 k + 35 } { k ^ { 2 } + 16 k + 63 } \cdot \frac { k ^ { 2 } + 9 k } { k ^ { 2 } + 9 k + 20 }$$

Accepted Answer

A)  $\frac { 1 } { k + 4 }$ 
B)  $\frac { k } { k ^ { 2 } + 16 k + 63 }$ 
C)  $\frac { k ^ { 2 } + 9 k } { k + 4 }$ 
D)  $\frac { k } { k + 4 }$ 
A)  $\frac { 1 } { k + 4 }$ 
B)  $\frac { k } { k ^ { 2 } + 16 k + 63 }$ 
C)  $\frac { k ^ { 2 } + 9 k } { k + 4 }$ 
D)  $\frac { k } { k + 4 }$

Question 3

Find all values that make the rational expression undefined. If the rational expression is defined for all real numbers, so
state.
-$$\frac { 6 } { 19 x }$$

Accepted Answer

A)  $x = - 19$ 
B)  $x = 6$ 
C)  $x = 0$ 
D)  Defined for all real numbers 
A)  $x = - 19$ 
B)  $x = 6$ 
C)  $x = 0$ 
D)  Defined for all real numbers

Question 4

Divide. Simplify if possible.
-$$\frac { x ^ { 2 } - 10 x + 25 } { 3 x - 15 } \div \frac { 6 x - 30 } { 18 }$$

Accepted Answer

A)  $\frac { x ^ { 2 } - 10 x + 25 } { ( x - 5 ) ^ { 2 } }$ 
B)  $\frac { ( x - 5 ) ^ { 2 } } { 9 }$ 
C)  1 
D)  18 
A)  $\frac { x ^ { 2 } - 10 x + 25 } { ( x - 5 ) ^ { 2 } }$ 
B)  $\frac { ( x - 5 ) ^ { 2 } } { 9 }$ 
C)  1 
D)  18

Question 5

Find the missing expression.
-$$\frac { 13 x + 3 } { x + 2 } - \frac { ? } { x + 2 } = \frac { 1 + 8 x } { x + 2 }$$

Accepted Answer

A)  $5 x + 2$ 
B)  $- 5 x + 4$ 
C)  $- 5 x - 4$ 
D)  $5 x - 2$ 
A)  $5 x + 2$ 
B)  $- 5 x + 4$ 
C)  $- 5 x - 4$ 
D)  $5 x - 2$

Question 6

Simplify the rational expression. If the rational expression cannot be simplified, so state.
-$$\frac { 81 - x ^ { 2 } } { x ^ { 2 } - 13 x + 36 }$$

Accepted Answer

A)  $- \frac { x + 9 } { x + 4 }$ 
B)  $- \frac { x - 9 } { x - 4 }$ 
C)  $- \frac { x + 9 } { x - 4 }$ 
D)  $\frac { x + 9 } { x - 4 }$ 
A)  $- \frac { x + 9 } { x + 4 }$ 
B)  $- \frac { x - 9 } { x - 4 }$ 
C)  $- \frac { x + 9 } { x - 4 }$ 
D)  $\frac { x + 9 } { x - 4 }$

Question 7

Perform the indicated operations. Simplify if possible.
-$$\left( \frac { 3 x ^ { 2 } - 4 x - 4 } { x ^ { 2 } + 2 x - 3 } \cdot \frac { x ^ { 2 } + 3 x - 4 } { 12 x ^ { 2 } + 11 x + 2 } \right) \div \frac { 3 x ^ { 2 } - 5 x - 2 } { 8 x ^ { 2 } - 2 x - 1 }$$

Accepted Answer

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

Question 8

Perform the indicated operation(s). Simplify if possible.
-$$\frac { 6 x + 7 y } { 2 } - \frac { 6 x - 7 y } { 2 }$$

Accepted Answer

A)  0 
B)  6x 
C)  49y 
D)  7y 
A)  0 
B)  6x 
C)  49y 
D)  7y

Question 9

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

Accepted Answer

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

Question 10

Simplify the rational expression. If the rational expression cannot be simplified, so state.
-$$\frac { 27 x - 24 } { 8 x - 9 x ^ { 2 } }$$

Accepted Answer

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

Question 11

Find the least common denominator of the rational expressions.
-$\frac { 7 } { x }$ and $\frac { 8 } { x - 6 }$

Accepted Answer

A)  $x ( x - 6 )$ 
B)  $x - 6$ 
C)  56 
D)  $x$ 
A)  $x ( x - 6 )$ 
B)  $x - 6$ 
C)  56 
D)  $x$

Question 12

Perform the indicated operation(s). Simplify if possible.
-$$\frac { 5 x } { x + 9 } + \frac { 3 x - 8 } { x + 9 } - \frac { 2 x } { x + 9 }$$

Accepted Answer

A)  $\frac { 6 x - 8 } { x + 9 }$ 
B)  $\frac { 6 x - 8 } { 3 x + 27 }$ 
C)  $\frac { 10 x - 8 } { x + 9 }$ 
D)  $\frac { 10 x + 8 } { x - 9 }$ 
A)  $\frac { 6 x - 8 } { x + 9 }$ 
B)  $\frac { 6 x - 8 } { 3 x + 27 }$ 
C)  $\frac { 10 x - 8 } { x + 9 }$ 
D)  $\frac { 10 x + 8 } { x - 9 }$

Question 13

Perform the indicated operation. Simplify if possible.
-$$\frac { x + 5 } { 13 } + \frac { 7 } { 13 }$$

Accepted Answer

A)  $\frac { x + 12 } { 26 }$ 
B)  $\frac { 12 x } { 26 }$ 
C)  $\frac { 12 x } { 13 }$ 
D)  $\frac { x + 12 } { 13 }$ 
A)  $\frac { x + 12 } { 26 }$ 
B)  $\frac { 12 x } { 26 }$ 
C)  $\frac { 12 x } { 13 }$ 
D)  $\frac { x + 12 } { 13 }$

Question 14

Perform the indicated operation(s). Simplify if possible.
-$\frac { 8 y ^ { 2 } - 6 y - 13 } { 25 y ^ { 2 } - 16 } - \frac { 3 y ^ { 2 } - 5 } { 25 y ^ { 2 } - 16 }$

Accepted Answer

A)  $\frac { y - 2 } { 5 y - 4 }$ 
B)  $\frac { 5 y - 4 } { 5 y + 4 }$ 
C)  $\frac { 8 y + 1 } { 5 y + 4 }$ 
D)  $\frac { 5 y + 4 } { 5 y - 4 }$ 
A)  $\frac { y - 2 } { 5 y - 4 }$ 
B)  $\frac { 5 y - 4 } { 5 y + 4 }$ 
C)  $\frac { 8 y + 1 } { 5 y + 4 }$ 
D)  $\frac { 5 y + 4 } { 5 y - 4 }$

Question 15

Find the least common denominator of the rational expressions.
-$\frac { 4 } { x ^ { 2 } + 7 x + 6 }$ and $\frac { 6 } { - 3 x - 18 }$

Accepted Answer

A)  $- 3 ( x - 1 ) ( x + 6 )$ 
B)  $- 3 ( x + 1 ) ( x - 6 )$ 
C)  $- 3 ( x - 1 ) ( x - 6 )$ 
D)  $- 3 ( x + 1 ) ( x + 6 )$ 
A)  $- 3 ( x - 1 ) ( x + 6 )$ 
B)  $- 3 ( x + 1 ) ( x - 6 )$ 
C)  $- 3 ( x - 1 ) ( x - 6 )$ 
D)  $- 3 ( x + 1 ) ( x + 6 )$

Question 16

Find all values that make the rational expression undefined. If the rational expression is defined for all real numbers, so
state.
-$$\frac { x ^ { 2 } - 64 } { x ^ { 2 } + 17 x + 70 }$$

Accepted Answer

A)  $x = 8 , x = - 8$ 
B)  $x = 7 , x = - 10$ 
C)  $x = - 7 , x = - 10$ 
D)  $x = 0$ 
A)  $x = 8 , x = - 8$ 
B)  $x = 7 , x = - 10$ 
C)  $x = - 7 , x = - 10$ 
D)  $x = 0$

Question 17

Add or subtract as indicated. Simplify the result, if possible.
-$$\frac { - 3 } { x ^ { 2 } - 25 } - \frac { 13 } { 25 - x ^ { 2 } }$$

Accepted Answer

A)  $\frac { 10 } { x ^ { 2 } - 25 }$ 
B)  $- \frac { 10 } { x ^ { 2 } - 25 }$ 
C)  $- \frac { 16 } { x ^ { 2 } - 25 }$ 
D)  $\frac { 16 } { x ^ { 2 } - 25 }$ 
A)  $\frac { 10 } { x ^ { 2 } - 25 }$ 
B)  $- \frac { 10 } { x ^ { 2 } - 25 }$ 
C)  $- \frac { 16 } { x ^ { 2 } - 25 }$ 
D)  $\frac { 16 } { x ^ { 2 } - 25 }$

Question 18

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

Accepted Answer

A)  $x = 2$ 
B)  $x = - 2$ 
C)  $x = 0$ 
D)  Defined for all real numbers 
A)  $x = 2$ 
B)  $x = - 2$ 
C)  $x = 0$ 
D)  Defined for all real numbers

Question 19

Perform the indicated operation(s). Simplify if possible.
-$$\frac { x } { x ^ { 2 } + 5 x - 24 } - \frac { 3 } { x ^ { 2 } + 5 x - 24 }$$

Accepted Answer

A)  $\frac { 1 } { 2 ( x + 8 ) }$ 
B)  $x - 3$ 
C)  $x + 8$ 
D)  $\frac { 1 } { x + 8 }$ 
A)  $\frac { 1 } { 2 ( x + 8 ) }$ 
B)  $x - 3$ 
C)  $x + 8$ 
D)  $\frac { 1 } { x + 8 }$

Question 20

Perform the indicated operation. Simplify if possible.
-$$\frac { 4 x - 6 } { x ^ { 2 } + 7 x + 10 } + \frac { 8 - 3 x } { x ^ { 2 } + 7 x + 10 }$$

Accepted Answer

A)  $\frac { x - 2 } { x ^ { 2 } + 7 x + 10 }$ 
B)  $\frac { 1 } { x + 5 }$ 
C)  $\frac { 1 } { x + 2 }$ 
D)  $\frac { 1 } { x ^ { 2 } + 7 x + 10 }$ 
A)  $\frac { x - 2 } { x ^ { 2 } + 7 x + 10 }$ 
B)  $\frac { 1 } { x + 5 }$ 
C)  $\frac { 1 } { x + 2 }$ 
D)  $\frac { 1 } { x ^ { 2 } + 7 x + 10 }$

Perform the indicated operation. Simplify if possible. -Express the perimeter of the rectangle as a fully simplified rational expression.

Multiply. Simplify if possible. - $\frac { k ^ { 2 } + 12 k + 35 } { k ^ { 2 } + 16 k + 63 } \cdot \frac { k ^ { 2 } + 9 k } { k ^ { 2 } + 9 k + 20 }$

Find all values that make the rational expression undefined. If the rational expression is defined for all real numbers, so state. - $\frac { 6 } { 19 x }$

Divide. Simplify if possible. - $\frac { x ^ { 2 } - 10 x + 25 } { 3 x - 15 } \div \frac { 6 x - 30 } { 18 }$

Find the missing expression. - $\frac { 13 x + 3 } { x + 2 } - \frac { ? } { x + 2 } = \frac { 1 + 8 x } { x + 2 }$

Simplify the rational expression. If the rational expression cannot be simplified, so state. - $\frac { 81 - x ^ { 2 } } { x ^ { 2 } - 13 x + 36 }$

Perform the indicated operations. Simplify if possible. - $\left( \frac { 3 x ^ { 2 } - 4 x - 4 } { x ^ { 2 } + 2 x - 3 } \cdot \frac { x ^ { 2 } + 3 x - 4 } { 12 x ^ { 2 } + 11 x + 2 } \right) \div \frac { 3 x ^ { 2 } - 5 x - 2 } { 8 x ^ { 2 } - 2 x - 1 }$

Perform the indicated operation(s). Simplify if possible. - $\frac { 6 x + 7 y } { 2 } - \frac { 6 x - 7 y } { 2 }$

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

Simplify the rational expression. If the rational expression cannot be simplified, so state. - $\frac { 27 x - 24 } { 8 x - 9 x ^ { 2 } }$

Find the least common denominator of the rational expressions. - $\frac { 7 } { x }$ and $\frac { 8 } { x - 6 }$

Perform the indicated operation(s). Simplify if possible. - $\frac { 5 x } { x + 9 } + \frac { 3 x - 8 } { x + 9 } - \frac { 2 x } { x + 9 }$

Perform the indicated operation. Simplify if possible. - $\frac { x + 5 } { 13 } + \frac { 7 } { 13 }$

Perform the indicated operation(s). Simplify if possible. - $\frac { 8 y ^ { 2 } - 6 y - 13 } { 25 y ^ { 2 } - 16 } - \frac { 3 y ^ { 2 } - 5 } { 25 y ^ { 2 } - 16 }$

Find the least common denominator of the rational expressions. - $\frac { 4 } { x ^ { 2 } + 7 x + 6 }$ and $\frac { 6 } { - 3 x - 18 }$

Find all values that make the rational expression undefined. If the rational expression is defined for all real numbers, so state. - $\frac { x ^ { 2 } - 64 } { x ^ { 2 } + 17 x + 70 }$

Add or subtract as indicated. Simplify the result, if possible. - $\frac { - 3 } { x ^ { 2 } - 25 } - \frac { 13 } { 25 - x ^ { 2 } }$

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

Perform the indicated operation(s). Simplify if possible. - $\frac { x } { x ^ { 2 } + 5 x - 24 } - \frac { 3 } { x ^ { 2 } + 5 x - 24 }$

Perform the indicated operation. Simplify if possible. - $\frac { 4 x - 6 } { x ^ { 2 } + 7 x + 10 } + \frac { 8 - 3 x } { x ^ { 2 } + 7 x + 10 }$

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

Perform the indicated operation. Simplify if possible. -Express the perimeter of the rectangle as a fully simplified rational expression.

Multiply. Simplify if possible. - k2+12k+35k2+16k+63⋅k2+9kk2+9k+20\frac { k ^ { 2 } + 12 k + 35 } { k ^ { 2 } + 16 k + 63 } \cdot \frac { k ^ { 2 } + 9 k } { k ^ { 2 } + 9 k + 20 }k2+16k+63k2+12k+35​⋅k2+9k+20k2+9k​

Find all values that make the rational expression undefined. If the rational expression is defined for all real numbers, so state. - 619x\frac { 6 } { 19 x }19x6​

Divide. Simplify if possible. - x2−10x+253x−15÷6x−3018\frac { x ^ { 2 } - 10 x + 25 } { 3 x - 15 } \div \frac { 6 x - 30 } { 18 }3x−15x2−10x+25​÷186x−30​

Find the missing expression. - 13x+3x+2−?x+2=1+8xx+2\frac { 13 x + 3 } { x + 2 } - \frac { ? } { x + 2 } = \frac { 1 + 8 x } { x + 2 }x+213x+3​−x+2?​=x+21+8x​

Simplify the rational expression. If the rational expression cannot be simplified, so state. - 81−x2x2−13x+36\frac { 81 - x ^ { 2 } } { x ^ { 2 } - 13 x + 36 }x2−13x+3681−x2​

Perform the indicated operation(s). Simplify if possible. - 6x+7y2−6x−7y2\frac { 6 x + 7 y } { 2 } - \frac { 6 x - 7 y } { 2 }26x+7y​−26x−7y​

Add or subtract as indicated. Simplify the result, if possible. - 2yx2−y2+2xy2−x2\frac { 2 y } { x ^ { 2 } - y ^ { 2 } } + \frac { 2 x } { y ^ { 2 } - x ^ { 2 } }x2−y22y​+y2−x22x​

Simplify the rational expression. If the rational expression cannot be simplified, so state. - 27x−248x−9x2\frac { 27 x - 24 } { 8 x - 9 x ^ { 2 } }8x−9x227x−24​

Find the least common denominator of the rational expressions. - 7x\frac { 7 } { x }x7​ and 8x−6\frac { 8 } { x - 6 }x−68​

Perform the indicated operation(s). Simplify if possible. - 5xx+9+3x−8x+9−2xx+9\frac { 5 x } { x + 9 } + \frac { 3 x - 8 } { x + 9 } - \frac { 2 x } { x + 9 }x+95x​+x+93x−8​−x+92x​

Perform the indicated operation. Simplify if possible. - x+513+713\frac { x + 5 } { 13 } + \frac { 7 } { 13 }13x+5​+137​

Perform the indicated operation(s). Simplify if possible. - 8y2−6y−1325y2−16−3y2−525y2−16\frac { 8 y ^ { 2 } - 6 y - 13 } { 25 y ^ { 2 } - 16 } - \frac { 3 y ^ { 2 } - 5 } { 25 y ^ { 2 } - 16 }25y2−168y2−6y−13​−25y2−163y2−5​

Find the least common denominator of the rational expressions. - 4x2+7x+6\frac { 4 } { x ^ { 2 } + 7 x + 6 }x2+7x+64​ and 6−3x−18\frac { 6 } { - 3 x - 18 }−3x−186​

Find all values that make the rational expression undefined. If the rational expression is defined for all real numbers, so state. - x2−64x2+17x+70\frac { x ^ { 2 } - 64 } { x ^ { 2 } + 17 x + 70 }x2+17x+70x2−64​

Add or subtract as indicated. Simplify the result, if possible. - −3x2−25−1325−x2\frac { - 3 } { x ^ { 2 } - 25 } - \frac { 13 } { 25 - x ^ { 2 } }x2−25−3​−25−x213​

Find all values that make the rational expression undefined. If the rational expression is defined for all real numbers, so state. - x−24\frac { x - 2 } { 4 }4x−2​

Perform the indicated operation(s). Simplify if possible. - xx2+5x−24−3x2+5x−24\frac { x } { x ^ { 2 } + 5 x - 24 } - \frac { 3 } { x ^ { 2 } + 5 x - 24 }x2+5x−24x​−x2+5x−243​

Perform the indicated operation. Simplify if possible. - 4x−6x2+7x+10+8−3xx2+7x+10\frac { 4 x - 6 } { x ^ { 2 } + 7 x + 10 } + \frac { 8 - 3 x } { x ^ { 2 } + 7 x + 10 }x2+7x+104x−6​+x2+7x+108−3x​