Question 1

Multiply. Simplify if possible.
-$$\frac { x ^ { 2 } - 5 x + 6 } { x ^ { 2 } - 11 x + 10 } \cdot \frac { x ^ { 2 } - 9 x + 8 } { x ^ { 2 } - 12 x + 27 }$$

Accepted Answer

A)  $\frac { ( x + 2 ) ( x + 8 ) } { ( x + 10 ) ( x + 9 ) }$ 
B)  $\frac { ( x - 2 ) } { ( x - 9 ) }$ 
C)  $\frac { ( x - 2 ) ( x - 8 ) } { ( x - 10 ) ( x - 9 ) }$ 
D)  $\frac { \left( x ^ { 2 } - 5 x + 6 \right) \left( x ^ { 2 } - 9 x + 8 \right) } { \left( x ^ { 2 } - 11 x + 10 \right) \left( x ^ { 2 } - 12 x + 27 \right) }$ 
A)  $\frac { ( x + 2 ) ( x + 8 ) } { ( x + 10 ) ( x + 9 ) }$ 
B)  $\frac { ( x - 2 ) } { ( x - 9 ) }$ 
C)  $\frac { ( x - 2 ) ( x - 8 ) } { ( x - 10 ) ( x - 9 ) }$ 
D)  $\frac { \left( x ^ { 2 } - 5 x + 6 \right) \left( x ^ { 2 } - 9 x + 8 \right) } { \left( x ^ { 2 } - 11 x + 10 \right) \left( x ^ { 2 } - 12 x + 27 \right) }$

Question 2

Add or subtract as indicated. Simplify the result, if possible.
-$$\frac { 8 } { x - 9 } + \frac { 6 } { 9 - x }$$

Accepted Answer

A)  $\frac { 2 } { 9 - x }$ 
B)  $- \frac { 2 } { x - 9 }$ 
C)  $\frac { 14 } { x - 9 }$ 
D)  $\frac { 2 } { x - 9 }$ 
A)  $\frac { 2 } { 9 - x }$ 
B)  $- \frac { 2 } { x - 9 }$ 
C)  $\frac { 14 } { x - 9 }$ 
D)  $\frac { 2 } { x - 9 }$

Question 3

Multiply. Simplify if possible.
-$$\frac { x ^ { 3 } + 1 } { x ^ { 3 } - x ^ { 2 } + x } \cdot \frac { 7 x } { - 35 x - 35 }$$

Accepted Answer

A)  $- \frac { 1 } { 5 }$ 
B)  $- \frac { x ^ { 3 } + 1 } { 5 ( x + 1 ) }$ 
C)  $\frac { x + 1 } { 5 ( - x - 1 ) }$ 
D)  $- \frac { x ^ { 2 } + 1 } { 5 }$ 
A)  $- \frac { 1 } { 5 }$ 
B)  $- \frac { x ^ { 3 } + 1 } { 5 ( x + 1 ) }$ 
C)  $\frac { x + 1 } { 5 ( - x - 1 ) }$ 
D)  $- \frac { x ^ { 2 } + 1 } { 5 }$

Question 4

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

Accepted Answer

A)  $\frac { 2 } { 9 }$ 
B)  $- \frac { 2 } { 9 }$ 
C)  cannot be simplified 
D)  1 
A)  $\frac { 2 } { 9 }$ 
B)  $- \frac { 2 } { 9 }$ 
C)  cannot be simplified 
D)  1

Question 5

Simplify the rational expression. If the rational expression cannot be simplified, so state.
-$$\frac { x ^ { 2 } + 6 x + 4 } { x ^ { 2 } + 7 x + 12 }$$

Accepted Answer

A)  $x + 2$ 
B)  $\frac { x + 2 } { x + 3 }$ 
C)  $\frac { x + 2 } { x + 4 }$ 
D)  cannot be simplified 
A)  $x + 2$ 
B)  $\frac { x + 2 } { x + 3 }$ 
C)  $\frac { x + 2 } { x + 4 }$ 
D)  cannot be simplified

Question 6

Find the least common denominator of the rational expressions.
-$\frac { 8 } { 12 x }$ and $\frac { 8 } { 9 x ^ { 2 } }$

Accepted Answer

A)  $36 x ^ { 2 }$ 
B)  $9 x ^ { 2 }$ 
C)  $36 \mathrm { x }$ 
D)  $36 x ^ { 3 }$ 
A)  $36 x ^ { 2 }$ 
B)  $9 x ^ { 2 }$ 
C)  $36 \mathrm { x }$ 
D)  $36 x ^ { 3 }$

Question 7

Simplify the rational expression. If the rational expression cannot be simplified, so state.
-$$\frac { 3 x - 5 } { 5 - 3 x }$$

Accepted Answer

A)  1 
B)  $- 1$ 
C)  $- \frac { 3 } { 5 }$ 
D)  cannot be simplified 
A)  1 
B)  $- 1$ 
C)  $- \frac { 3 } { 5 }$ 
D)  cannot be simplified

Question 8

Simplify the rational expression. If the rational expression cannot be simplified, so state.
-$\frac { - 14 } { 2 x - 10 }$

Accepted Answer

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

Question 9

Find the least common denominator of the rational expressions.
-$\frac { 1 } { x ^ { 2 } + 16 x + 64 }$ and $\frac { 1 } { x ^ { 2 } + 8 x }$

Accepted Answer

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

Question 10

Perform the indicated operation. Simplify if possible.
-$$\frac { 26 x - 72 } { 3 x + 18 } + \frac { 144 - 14 x } { 3 x + 18 }$$

Accepted Answer

A)  $- 4$ 
B)  8 
C)  4 
D)  2 
A)  $- 4$ 
B)  8 
C)  4 
D)  2

Question 11

Find all values that make the rational expression undefined. If the rational expression is defined for all real numbers, so
state.
-$$\frac { 4 x ^ { 2 } - 16 } { 6 x - 42 }$$

Accepted Answer

A)  $x = 2 , x = - 2$ 
B)  $x = 7$ 
C)  $x = 42$ 
D)  Defined for all real numbers 
A)  $x = 2 , x = - 2$ 
B)  $x = 7$ 
C)  $x = 42$ 
D)  Defined for all real numbers

Question 12

Simplify the rational expression. If the rational expression cannot be simplified, so state.
-$$\frac { x ^ { 2 } + 11 x y + 18 y ^ { 2 } } { x ^ { 2 } + 16 x y + 63 y ^ { 2 } }$$

Accepted Answer

A)  $\frac { x + 2 y } { x + 7 y }$ 
B)  $\frac { 11 x + 18 y } { 16 x + 63 y }$ 
C)  cannot be simplified 
D)  $\frac { x + 7 y } { x + 2 y }$ 
A)  $\frac { x + 2 y } { x + 7 y }$ 
B)  $\frac { 11 x + 18 y } { 16 x + 63 y }$ 
C)  cannot be simplified 
D)  $\frac { x + 7 y } { x + 2 y }$

Question 13

Simplify the rational expression. If the rational expression cannot be simplified, so state.
-$$\frac { y ^ { 3 } - 343 } { y - 7 }$$

Accepted Answer

A)  cannot be simplified 
B)  $y ^ { 2 } - 49$ 
C)  $y ^ { 2 } + 7 y + 49$ 
D)  $\frac { 1 } { y - 7 }$ 
A)  cannot be simplified 
B)  $y ^ { 2 } - 49$ 
C)  $y ^ { 2 } + 7 y + 49$ 
D)  $\frac { 1 } { y - 7 }$

Question 14

Add or subtract as indicated. Simplify the result, if possible.
-$$\frac { 8 } { x + 3 } - \frac { 4 } { - x - 3 }$$

Accepted Answer

A)  $- \frac { 12 } { x + 3 }$ 
B)  $\frac { 12 } { x + 3 }$ 
C)  $\frac { 4 } { x + 3 }$ 
D)  $\frac { 4 } { x - 3 }$ 
A)  $- \frac { 12 } { x + 3 }$ 
B)  $\frac { 12 } { x + 3 }$ 
C)  $\frac { 4 } { x + 3 }$ 
D)  $\frac { 4 } { x - 3 }$

Question 15

Simplify the rational expression. If the rational expression cannot be simplified, so state.
-$\frac { 3 x - 12 } { 27 }$

Accepted Answer

A)  $\frac { x + 12 } { 9 }$ 
B)  $\frac { x + 4 } { 9 }$ 
C)  $\frac { x - 4 } { 9 }$ 
D)  $\frac { x - 12 } { 9 }$ 
A)  $\frac { x + 12 } { 9 }$ 
B)  $\frac { x + 4 } { 9 }$ 
C)  $\frac { x - 4 } { 9 }$ 
D)  $\frac { x - 12 } { 9 }$

Multiply. Simplify if possible. - $\frac { x ^ { 2 } - 5 x + 6 } { x ^ { 2 } - 11 x + 10 } \cdot \frac { x ^ { 2 } - 9 x + 8 } { x ^ { 2 } - 12 x + 27 }$

Add or subtract as indicated. Simplify the result, if possible. - $\frac { 8 } { x - 9 } + \frac { 6 } { 9 - x }$

Multiply. Simplify if possible. - $\frac { x ^ { 3 } + 1 } { x ^ { 3 } - x ^ { 2 } + x } \cdot \frac { 7 x } { - 35 x - 35 }$

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

Simplify the rational expression. If the rational expression cannot be simplified, so state. - $\frac { x ^ { 2 } + 6 x + 4 } { x ^ { 2 } + 7 x + 12 }$

Find the least common denominator of the rational expressions. - $\frac { 8 } { 12 x }$ and $\frac { 8 } { 9 x ^ { 2 } }$

Simplify the rational expression. If the rational expression cannot be simplified, so state. - $\frac { 3 x - 5 } { 5 - 3 x }$

Simplify the rational expression. If the rational expression cannot be simplified, so state. - $\frac { - 14 } { 2 x - 10 }$

Find the least common denominator of the rational expressions. - $\frac { 1 } { x ^ { 2 } + 16 x + 64 }$ and $\frac { 1 } { x ^ { 2 } + 8 x }$

Perform the indicated operation. Simplify if possible. - $\frac { 26 x - 72 } { 3 x + 18 } + \frac { 144 - 14 x } { 3 x + 18 }$

Find all values that make the rational expression undefined. If the rational expression is defined for all real numbers, so state. - $\frac { 4 x ^ { 2 } - 16 } { 6 x - 42 }$

Simplify the rational expression. If the rational expression cannot be simplified, so state. - $\frac { x ^ { 2 } + 11 x y + 18 y ^ { 2 } } { x ^ { 2 } + 16 x y + 63 y ^ { 2 } }$

Simplify the rational expression. If the rational expression cannot be simplified, so state. - $\frac { y ^ { 3 } - 343 } { y - 7 }$

Add or subtract as indicated. Simplify the result, if possible. - $\frac { 8 } { x + 3 } - \frac { 4 } { - x - 3 }$

Simplify the rational expression. If the rational expression cannot be simplified, so state. - $\frac { 3 x - 12 } { 27 }$

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

Multiply. Simplify if possible. - x2−5x+6x2−11x+10⋅x2−9x+8x2−12x+27\frac { x ^ { 2 } - 5 x + 6 } { x ^ { 2 } - 11 x + 10 } \cdot \frac { x ^ { 2 } - 9 x + 8 } { x ^ { 2 } - 12 x + 27 }x2−11x+10x2−5x+6​⋅x2−12x+27x2−9x+8​

Add or subtract as indicated. Simplify the result, if possible. - 8x−9+69−x\frac { 8 } { x - 9 } + \frac { 6 } { 9 - x }x−98​+9−x6​

Multiply. Simplify if possible. - x3+1x3−x2+x⋅7x−35x−35\frac { x ^ { 3 } + 1 } { x ^ { 3 } - x ^ { 2 } + x } \cdot \frac { 7 x } { - 35 x - 35 }x3−x2+xx3+1​⋅−35x−357x​

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

Simplify the rational expression. If the rational expression cannot be simplified, so state. - x2+6x+4x2+7x+12\frac { x ^ { 2 } + 6 x + 4 } { x ^ { 2 } + 7 x + 12 }x2+7x+12x2+6x+4​

Find the least common denominator of the rational expressions. - 812x\frac { 8 } { 12 x }12x8​ and 89x2\frac { 8 } { 9 x ^ { 2 } }9x28​

Simplify the rational expression. If the rational expression cannot be simplified, so state. - 3x−55−3x\frac { 3 x - 5 } { 5 - 3 x }5−3x3x−5​

Simplify the rational expression. If the rational expression cannot be simplified, so state. - −142x−10\frac { - 14 } { 2 x - 10 }2x−10−14​

Find the least common denominator of the rational expressions. - 1x2+16x+64\frac { 1 } { x ^ { 2 } + 16 x + 64 }x2+16x+641​ and 1x2+8x\frac { 1 } { x ^ { 2 } + 8 x }x2+8x1​

Perform the indicated operation. Simplify if possible. - 26x−723x+18+144−14x3x+18\frac { 26 x - 72 } { 3 x + 18 } + \frac { 144 - 14 x } { 3 x + 18 }3x+1826x−72​+3x+18144−14x​

Find all values that make the rational expression undefined. If the rational expression is defined for all real numbers, so state. - 4x2−166x−42\frac { 4 x ^ { 2 } - 16 } { 6 x - 42 }6x−424x2−16​

Simplify the rational expression. If the rational expression cannot be simplified, so state. - x2+11xy+18y2x2+16xy+63y2\frac { x ^ { 2 } + 11 x y + 18 y ^ { 2 } } { x ^ { 2 } + 16 x y + 63 y ^ { 2 } }x2+16xy+63y2x2+11xy+18y2​

Simplify the rational expression. If the rational expression cannot be simplified, so state. - y3−343y−7\frac { y ^ { 3 } - 343 } { y - 7 }y−7y3−343​

Add or subtract as indicated. Simplify the result, if possible. - 8x+3−4−x−3\frac { 8 } { x + 3 } - \frac { 4 } { - x - 3 }x+38​−−x−34​

Simplify the rational expression. If the rational expression cannot be simplified, so state. - 3x−1227\frac { 3 x - 12 } { 27 }273x−12​