Question 1

Simplify.
-$$\frac { 2 x + 2 } { 6 x ^ { 2 } + 16 x + 10 }$$

Accepted Answer

A)  $\frac { 2 x + 3 } { 3 x + 16 }$ 
B)  $\frac { 2 x + 2 } { 6 x ^ { 2 } + 16 x + 10 }$ 
C)  $\frac { 2 x } { 3 x + 5 }$ 
D)  $\frac { 1 } { 3 x + 5 }$ 
A)  $\frac { 2 x + 3 } { 3 x + 16 }$ 
B)  $\frac { 2 x + 2 } { 6 x ^ { 2 } + 16 x + 10 }$ 
C)  $\frac { 2 x } { 3 x + 5 }$ 
D)  $\frac { 1 } { 3 x + 5 }$

Question 2

Perform the operation indicated.
-$\frac { 3 x } { 6 x + 3 } \cdot \frac { 10 x + 5 } { 4 }$

Accepted Answer

A)  $\frac { 5 x } { 4 }$ 
B)  $\frac { 5 x } { 12 }$ 
C)  $\frac { x } { 4 }$ 
D)  $\frac { 5 } { 4 }$ 
A)  $\frac { 5 x } { 4 }$ 
B)  $\frac { 5 x } { 12 }$ 
C)  $\frac { x } { 4 }$ 
D)  $\frac { 5 } { 4 }$

Question 3

Simplify.
-$$\frac { 6 - 2 x } { 7 x ^ { 2 } - 21 x }$$

Accepted Answer

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

Question 4

Perform the operation indicated.
-$$\frac { ( x - 9 ) ^ { 2 } } { 3 } \div \frac { 3 x - 27 } { 9 }$$

Accepted Answer

A)  $\frac { 3 ( x - 9 ) ^ { 2 } } { 3 x - 27 }$ 
B)  $x - 9$ 
C)  $\frac { 1 } { x - 9 }$ 
D)  $\frac { ( x - 9 ) ^ { 3 } } { 9 }$ 
A)  $\frac { 3 ( x - 9 ) ^ { 2 } } { 3 x - 27 }$ 
B)  $x - 9$ 
C)  $\frac { 1 } { x - 9 }$ 
D)  $\frac { ( x - 9 ) ^ { 3 } } { 9 }$

Question 5

Perform the operation indicated. Simplify.
-$$\frac { \frac { 8 } { x y } } { \frac { 5 } { x } + \frac { 4 } { y } }$$

Accepted Answer

A)  $\frac { 8 } { 5 x + 4 y }$ 
B)  $\frac { 8 x y } { 4 x + 5 y }$ 
C)  $\frac { 4 x + 5 y } { 8 }$ 
D)  $\frac { 8 } { 4 x + 5 y }$ 
A)  $\frac { 8 } { 5 x + 4 y }$ 
B)  $\frac { 8 x y } { 4 x + 5 y }$ 
C)  $\frac { 4 x + 5 y } { 8 }$ 
D)  $\frac { 8 } { 4 x + 5 y }$

Question 6

Simplify.
-$\frac { 3 x + 6 } { 2 x + 4 }$

Accepted Answer

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

Question 7

Find the LCD. Do not combine fractions.
-$$\frac { 2 } { 4 x - 32 } , \frac { 6 } { x ^ { 2 } - 8 x }$$

Accepted Answer

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

Question 8

Find the LCD. Do not combine fractions.
-$$\frac { 18 x + 3 } { 15 x - 8 } , \frac { 5 x } { 15 x + 8 }$$

Accepted Answer

A)  $( 15 x - 8 ) ( 15 x + 8 )$ 
B)  $( 15 x - 8 )$ or $( 15 x + 8 )$ 
C)  $5 x ( 18 x + 3 ) ( 15 x - 8 ) ( 15 x + 8 )$ 
D)  $5 x ( 18 x + 3 )$ 
A)  $( 15 x - 8 ) ( 15 x + 8 )$ 
B)  $( 15 x - 8 )$ or $( 15 x + 8 )$ 
C)  $5 x ( 18 x + 3 ) ( 15 x - 8 ) ( 15 x + 8 )$ 
D)  $5 x ( 18 x + 3 )$

Question 9

Find the LCD. Do not combine fractions.
-$$\frac { 3 } { x ^ { 2 } - 4 x - 5 } , \frac { 5 } { 3 x - 15 }$$

Accepted Answer

A)  $3 ( x - 1 ) ( x + 5 )$ 
B)  $3 ( x - 1 ) ( x - 5 )$ 
C)  $3 ( x + 1 ) ( x - 5 )$ 
D)  $3 ( x + 1 ) ( x + 5 )$ 
A)  $3 ( x - 1 ) ( x + 5 )$ 
B)  $3 ( x - 1 ) ( x - 5 )$ 
C)  $3 ( x + 1 ) ( x - 5 )$ 
D)  $3 ( x + 1 ) ( x + 5 )$

Question 10

Find the LCD. Do not combine fractions.
-$$\frac { 3 } { x ^ { 2 } - 49 } , \frac { 11 } { x - 7 }$$

Accepted Answer

A)  $x - 7$ 
B)  $x ^ { 2 } - 49$ 
C)  $( x - 7 ) \left( x ^ { 2 } - 49 \right)$ 
D)  $( x - 7 ) ^ { 3 }$ 
A)  $x - 7$ 
B)  $x ^ { 2 } - 49$ 
C)  $( x - 7 ) \left( x ^ { 2 } - 49 \right)$ 
D)  $( x - 7 ) ^ { 3 }$

Question 11

Perform the operation indicated.
-$$\frac { x ^ { 2 } + 7 x + 12 } { x ^ { 2 } + 10 x + 24 } \cdot \frac { x ^ { 2 } + 6 x } { x ^ { 2 } + 8 x + 15 }$$

Accepted Answer

A)  $\frac { x } { x ^ { 2 } + 10 x + 24 }$ 
B)  $\frac { x ^ { 2 } + 6 x } { x + 5 }$ 
C)  $\frac { 1 } { x + 5 }$ 
D)  $\frac { x } { x + 5 }$ 
A)  $\frac { x } { x ^ { 2 } + 10 x + 24 }$ 
B)  $\frac { x ^ { 2 } + 6 x } { x + 5 }$ 
C)  $\frac { 1 } { x + 5 }$ 
D)  $\frac { x } { x + 5 }$

Question 12

Perform the operation indicated.
-$$\frac { x ^ { 2 } + 11 x + 18 } { x ^ { 2 } + 18 x + 81 } \div \frac { x ^ { 2 } + 2 x } { x ^ { 2 } + 14 x + 45 }$$

Accepted Answer

A)  $\frac { x + 5 } { x }$ 
B)  $x + 5$ 
C)  $\frac { x } { x ^ { 2 } + 18 x + 81 }$ 
D)  $\frac { x + 5 } { x ^ { 2 } + 9 x }$ 
A)  $\frac { x + 5 } { x }$ 
B)  $x + 5$ 
C)  $\frac { x } { x ^ { 2 } + 18 x + 81 }$ 
D)  $\frac { x + 5 } { x ^ { 2 } + 9 x }$

Question 13

Find the LCD. Do not combine fractions.
-$$\frac { 9 } { x } , \frac { 4 } { x + 1 }$$

Accepted Answer

A)  $x$ 
B)  36 
C)  $x + 1$ 
D)  $x ( x + 1 )$ 
A)  $x$ 
B)  36 
C)  $x + 1$ 
D)  $x ( x + 1 )$

Question 14

Perform the operation indicated. Simplify.
-$$\frac { \frac { 6 } { x } + \frac { 5 } { y } } { 5 x + 6 y }$$

Accepted Answer

A)  $\frac { 5 x + 6 y } { x y }$ 
B)  $x y$ 
C)  $\frac { 1 } { x y }$ 
D)  $\frac { 6 x + 5 y } { 5 x + 6 y }$ 
A)  $\frac { 5 x + 6 y } { x y }$ 
B)  $x y$ 
C)  $\frac { 1 } { x y }$ 
D)  $\frac { 6 x + 5 y } { 5 x + 6 y }$

Question 15

Perform the operation indicated. Simplify.
-$$\frac { x - 2 } { x ^ { 2 } + 6 x + 5 } + \frac { 2 x + 5 } { x ^ { 2 } + 4 x + 3 }$$

Accepted Answer

A)  $\frac { 3 x ^ { 2 } + 16 x + 19 } { ( x - 1 ) ( x - 5 ) ( x - 3 ) }$ 
B)  $3 x + 3$ 
C)  $\frac { 3 x ^ { 2 } + 16 x + 19 } { ( x + 1 ) ( x + 5 ) ( x + 3 ) }$ 
D)  $\frac { 3 x + 3 } { 2 x ^ { 2 } + 10 x + 8 }$ 
A)  $\frac { 3 x ^ { 2 } + 16 x + 19 } { ( x - 1 ) ( x - 5 ) ( x - 3 ) }$ 
B)  $3 x + 3$ 
C)  $\frac { 3 x ^ { 2 } + 16 x + 19 } { ( x + 1 ) ( x + 5 ) ( x + 3 ) }$ 
D)  $\frac { 3 x + 3 } { 2 x ^ { 2 } + 10 x + 8 }$

Question 16

Perform the operation indicated.
-$$\frac { 14 x ^ { 2 } - 23 x y - 30 y ^ { 2 } } { 49 x ^ { 2 } + 63 x y + 18 y ^ { 2 } } + \frac { 10 x ^ { 2 } - 37 x y + 30 y ^ { 2 } } { 20 x ^ { 2 } - 49 x y + 30 y ^ { 2 } }$$

Accepted Answer

A)  $\frac { ( 7 x - 3 y ) } { ( 4 x + 5 y ) }$ 
B)  $\frac { ( 2 x + 5 y ) ^ { 2 } } { ( 4 x + 5 y ) ( 7 x - 3 y ) }$ 
C)  $\frac { 4 x - 5 y } { 7 x + 3 y }$ 
D)  $\frac { ( 2 x - 5 y ) ^ { 2 } } { ( 4 x - 5 y ) ( 7 x + 3 y ) }$ 
A)  $\frac { ( 7 x - 3 y ) } { ( 4 x + 5 y ) }$ 
B)  $\frac { ( 2 x + 5 y ) ^ { 2 } } { ( 4 x + 5 y ) ( 7 x - 3 y ) }$ 
C)  $\frac { 4 x - 5 y } { 7 x + 3 y }$ 
D)  $\frac { ( 2 x - 5 y ) ^ { 2 } } { ( 4 x - 5 y ) ( 7 x + 3 y ) }$

Question 17

Perform the operation indicated. Simplify.
-$$\frac { x - 5 } { x ^ { 2 } - 4 x + 3 } + \frac { 2 x + 1 } { x ^ { 2 } - 7 x + 6 }$$

Accepted Answer

A)  $\frac { 3 x - 4 } { 2 x ^ { 2 } - 11 x + 9 }$ 
B)  $\frac { 3 x ^ { 2 } - 16 x + 27 } { ( x + 1 ) ( x + 3 ) ( x + 6 ) }$ 
C)  $3 x - 4$ 
D)  $\frac { 3 x ^ { 2 } - 16 x + 27 } { ( x - 1 ) ( x - 3 ) ( x - 6 ) }$ 
A)  $\frac { 3 x - 4 } { 2 x ^ { 2 } - 11 x + 9 }$ 
B)  $\frac { 3 x ^ { 2 } - 16 x + 27 } { ( x + 1 ) ( x + 3 ) ( x + 6 ) }$ 
C)  $3 x - 4$ 
D)  $\frac { 3 x ^ { 2 } - 16 x + 27 } { ( x - 1 ) ( x - 3 ) ( x - 6 ) }$

Question 18

Perform the operation indicated. Simplify.
-$$\frac { 4 } { 11 + x } + \frac { x + 2 } { 11 + x }$$

Accepted Answer

A)  $\frac { 6 } { 11 }$ 
B)  $\frac { x + 6 } { 22 + x }$ 
C)  $\frac { 6 } { 22 }$ 
D)  $\frac { x + 6 } { 11 + x }$ 
A)  $\frac { 6 } { 11 }$ 
B)  $\frac { x + 6 } { 22 + x }$ 
C)  $\frac { 6 } { 22 }$ 
D)  $\frac { x + 6 } { 11 + x }$

Question 19

Perform the operation indicated.
-$$\frac { 3 x - 3 } { x } + \frac { 7 x - 7 } { 4 x ^ { 2 } }$$

Accepted Answer

A)  $\frac { 7 } { 12 x }$ 
B)  $\frac { 12 x ^ { 3 } - 12 x ^ { 2 } } { 7 x ^ { 2 } - 7 x }$ 
C)  $\frac { 21 x ^ { 2 } + 42 x + 21 } { 4 x ^ { 3 } }$ 
D)  $\frac { 12 x } { 7 }$ 
A)  $\frac { 7 } { 12 x }$ 
B)  $\frac { 12 x ^ { 3 } - 12 x ^ { 2 } } { 7 x ^ { 2 } - 7 x }$ 
C)  $\frac { 21 x ^ { 2 } + 42 x + 21 } { 4 x ^ { 3 } }$ 
D)  $\frac { 12 x } { 7 }$

Question 20

Perform the operation indicated. Simplify.
-$$\frac { 13 } { x - 5 } + \frac { x } { x ^ { 2 } - 25 }$$

Accepted Answer

A)  $\frac { 14 x + 65 } { ( x + 5 ) ( x - 5 ) }$ 
B)  $\frac { 14 x - 65 } { ( x + 5 ) ( x - 5 ) }$ 
C)  $\frac { 13 x + 65 } { ( x + 5 ) ( x - 5 ) }$ 
D)  $\frac { 13 x } { ( x + 5 ) ( x - 5 ) }$ 
A)  $\frac { 14 x + 65 } { ( x + 5 ) ( x - 5 ) }$ 
B)  $\frac { 14 x - 65 } { ( x + 5 ) ( x - 5 ) }$ 
C)  $\frac { 13 x + 65 } { ( x + 5 ) ( x - 5 ) }$ 
D)  $\frac { 13 x } { ( x + 5 ) ( x - 5 ) }$

Simplify. - $\frac { 2 x + 2 } { 6 x ^ { 2 } + 16 x + 10 }$

Perform the operation indicated. - $\frac { 3 x } { 6 x + 3 } \cdot \frac { 10 x + 5 } { 4 }$

Simplify. - $\frac { 6 - 2 x } { 7 x ^ { 2 } - 21 x }$

Perform the operation indicated. - $\frac { ( x - 9 ) ^ { 2 } } { 3 } \div \frac { 3 x - 27 } { 9 }$

Perform the operation indicated. Simplify. - $\frac { \frac { 8 } { x y } } { \frac { 5 } { x } + \frac { 4 } { y } }$

Simplify. - $\frac { 3 x + 6 } { 2 x + 4 }$

Find the LCD. Do not combine fractions. - $\frac { 2 } { 4 x - 32 } , \frac { 6 } { x ^ { 2 } - 8 x }$

Find the LCD. Do not combine fractions. - $\frac { 18 x + 3 } { 15 x - 8 } , \frac { 5 x } { 15 x + 8 }$

Find the LCD. Do not combine fractions. - $\frac { 3 } { x ^ { 2 } - 4 x - 5 } , \frac { 5 } { 3 x - 15 }$

Find the LCD. Do not combine fractions. - $\frac { 3 } { x ^ { 2 } - 49 } , \frac { 11 } { x - 7 }$

Perform the operation indicated. - $\frac { x ^ { 2 } + 7 x + 12 } { x ^ { 2 } + 10 x + 24 } \cdot \frac { x ^ { 2 } + 6 x } { x ^ { 2 } + 8 x + 15 }$

Perform the operation indicated. - $\frac { x ^ { 2 } + 11 x + 18 } { x ^ { 2 } + 18 x + 81 } \div \frac { x ^ { 2 } + 2 x } { x ^ { 2 } + 14 x + 45 }$

Find the LCD. Do not combine fractions. - $\frac { 9 } { x } , \frac { 4 } { x + 1 }$

Perform the operation indicated. Simplify. - $\frac { \frac { 6 } { x } + \frac { 5 } { y } } { 5 x + 6 y }$

Perform the operation indicated. Simplify. - $\frac { x - 2 } { x ^ { 2 } + 6 x + 5 } + \frac { 2 x + 5 } { x ^ { 2 } + 4 x + 3 }$

Perform the operation indicated. - $\frac { 14 x ^ { 2 } - 23 x y - 30 y ^ { 2 } } { 49 x ^ { 2 } + 63 x y + 18 y ^ { 2 } } + \frac { 10 x ^ { 2 } - 37 x y + 30 y ^ { 2 } } { 20 x ^ { 2 } - 49 x y + 30 y ^ { 2 } }$

Perform the operation indicated. Simplify. - $\frac { x - 5 } { x ^ { 2 } - 4 x + 3 } + \frac { 2 x + 1 } { x ^ { 2 } - 7 x + 6 }$

Perform the operation indicated. Simplify. - $\frac { 4 } { 11 + x } + \frac { x + 2 } { 11 + x }$

Perform the operation indicated. - $\frac { 3 x - 3 } { x } + \frac { 7 x - 7 } { 4 x ^ { 2 } }$

Perform the operation indicated. Simplify. - $\frac { 13 } { x - 5 } + \frac { x } { x ^ { 2 } - 25 }$

Real Numbers and Variables

Equations, Inequalities, and Applications

Graphing and Functions

Systems of Linear Equations and Inequalities

Exponents and Polynomials

Factoring

Rational Exponents and Radicals

Quadratic Equations and Inequalities

The Conic Sections

Additional Properties of Functions

Logarithmic and Exponential Functions

Filters

Exam 7: Rational Expressions and Equations

Simplify. - 2x+26x2+16x+10\frac { 2 x + 2 } { 6 x ^ { 2 } + 16 x + 10 }6x2+16x+102x+2​

Perform the operation indicated. - 3x6x+3⋅10x+54\frac { 3 x } { 6 x + 3 } \cdot \frac { 10 x + 5 } { 4 }6x+33x​⋅410x+5​

Simplify. - 6−2x7x2−21x\frac { 6 - 2 x } { 7 x ^ { 2 } - 21 x }7x2−21x6−2x​

Perform the operation indicated. - (x−9)23÷3x−279\frac { ( x - 9 ) ^ { 2 } } { 3 } \div \frac { 3 x - 27 } { 9 }3(x−9)2​÷93x−27​

Perform the operation indicated. Simplify. - 8xy5x+4y\frac { \frac { 8 } { x y } } { \frac { 5 } { x } + \frac { 4 } { y } }x5​+y4​xy8​​

Simplify. - 3x+62x+4\frac { 3 x + 6 } { 2 x + 4 }2x+43x+6​

Find the LCD. Do not combine fractions. - 24x−32,6x2−8x\frac { 2 } { 4 x - 32 } , \frac { 6 } { x ^ { 2 } - 8 x }4x−322​,x2−8x6​

Find the LCD. Do not combine fractions. - 18x+315x−8,5x15x+8\frac { 18 x + 3 } { 15 x - 8 } , \frac { 5 x } { 15 x + 8 }15x−818x+3​,15x+85x​

Find the LCD. Do not combine fractions. - 3x2−4x−5,53x−15\frac { 3 } { x ^ { 2 } - 4 x - 5 } , \frac { 5 } { 3 x - 15 }x2−4x−53​,3x−155​

Find the LCD. Do not combine fractions. - 3x2−49,11x−7\frac { 3 } { x ^ { 2 } - 49 } , \frac { 11 } { x - 7 }x2−493​,x−711​

Perform the operation indicated. - x2+7x+12x2+10x+24⋅x2+6xx2+8x+15\frac { x ^ { 2 } + 7 x + 12 } { x ^ { 2 } + 10 x + 24 } \cdot \frac { x ^ { 2 } + 6 x } { x ^ { 2 } + 8 x + 15 }x2+10x+24x2+7x+12​⋅x2+8x+15x2+6x​

Perform the operation indicated. - x2+11x+18x2+18x+81÷x2+2xx2+14x+45\frac { x ^ { 2 } + 11 x + 18 } { x ^ { 2 } + 18 x + 81 } \div \frac { x ^ { 2 } + 2 x } { x ^ { 2 } + 14 x + 45 }x2+18x+81x2+11x+18​÷x2+14x+45x2+2x​

Find the LCD. Do not combine fractions. - 9x,4x+1\frac { 9 } { x } , \frac { 4 } { x + 1 }x9​,x+14​

Perform the operation indicated. Simplify. - 6x+5y5x+6y\frac { \frac { 6 } { x } + \frac { 5 } { y } } { 5 x + 6 y }5x+6yx6​+y5​​

Perform the operation indicated. Simplify. - x−2x2+6x+5+2x+5x2+4x+3\frac { x - 2 } { x ^ { 2 } + 6 x + 5 } + \frac { 2 x + 5 } { x ^ { 2 } + 4 x + 3 }x2+6x+5x−2​+x2+4x+32x+5​

Perform the operation indicated. Simplify. - x−5x2−4x+3+2x+1x2−7x+6\frac { x - 5 } { x ^ { 2 } - 4 x + 3 } + \frac { 2 x + 1 } { x ^ { 2 } - 7 x + 6 }x2−4x+3x−5​+x2−7x+62x+1​

Perform the operation indicated. Simplify. - 411+x+x+211+x\frac { 4 } { 11 + x } + \frac { x + 2 } { 11 + x }11+x4​+11+xx+2​

Perform the operation indicated. - 3x−3x+7x−74x2\frac { 3 x - 3 } { x } + \frac { 7 x - 7 } { 4 x ^ { 2 } }x3x−3​+4x27x−7​

Perform the operation indicated. Simplify. - 13x−5+xx2−25\frac { 13 } { x - 5 } + \frac { x } { x ^ { 2 } - 25 }x−513​+x2−25x​