Question 1

Find the quotient and simplify.
-$\frac { z ^ { 2 } + 8 z + 16 } { z ^ { 2 } + 11 z + 28 } \div \frac { z ^ { 2 } + 4 z } { z ^ { 2 } + 17 z + 70 }$

Accepted Answer

A)  $\frac { \mathrm { z } + 10 } { \mathrm { z } ^ { 2 } + 7 \mathrm { z } }$ 
B)  $\frac { z + 10 } { z }$ 
C)  $\frac { z } { z ^ { 2 } + 11 z + 28 }$ 
D)  $z + 10$ 
A)  $\frac { \mathrm { z } + 10 } { \mathrm { z } ^ { 2 } + 7 \mathrm { z } }$ 
B)  $\frac { z + 10 } { z }$ 
C)  $\frac { z } { z ^ { 2 } + 11 z + 28 }$ 
D)  $z + 10$

Question 2

Solve the problem.
-If $f ( x ) = \frac { x ^ { 2 } - 2 } { x ^ { 3 } + 3 x }$, find $f ( 2 )$

Accepted Answer

A)  $\frac { 2 } { 7 }$ 
B)  $\frac { 1 } { 7 }$ 
C)  $\frac { 2 } { 11 }$ 
D)  $\frac { 1 } { 4 }$ 
A)  $\frac { 2 } { 7 }$ 
B)  $\frac { 1 } { 7 }$ 
C)  $\frac { 2 } { 11 }$ 
D)  $\frac { 1 } { 4 }$

Question 3

Simplify.
-$\frac { \frac { x } { 8 } } { \frac { 3 } { x + 7 } }$

Accepted Answer

A)  $\frac { 8 x } { 3 ( x + 7 ) }$ 
B)  $24 x ( x + 7 )$ 
C)  $\frac { x ( x + 7 ) } { 24 }$ 
D)  $\frac { x + 7 } { 24 x }$ 
A)  $\frac { 8 x } { 3 ( x + 7 ) }$ 
B)  $24 x ( x + 7 )$ 
C)  $\frac { x ( x + 7 ) } { 24 }$ 
D)  $\frac { x + 7 } { 24 x }$

Question 4

Perform the indicated operation. Simplify if possible.
-$\frac { x } { 14 } + \frac { 13 } { 14 }$

Accepted Answer

A)  $\frac { x + 13 } { 28 }$ 
B)  $\frac { 13 x } { 14 }$ 
C)  $\frac { x + 13 } { 14 }$ 
D)  $\frac { 13 x } { 28 }$ 
A)  $\frac { x + 13 } { 28 }$ 
B)  $\frac { 13 x } { 14 }$ 
C)  $\frac { x + 13 } { 14 }$ 
D)  $\frac { 13 x } { 28 }$

Question 5

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

Accepted Answer

A)  $\frac { 0 x + 12 } { 2 x }$ 
B)  $\frac { 0 x - 16 } { 2 x }$ 
C)  $\frac { 16 x - 16 } { 2 x }$ 
D)  $\frac { 0 x - 16 } { 2 x ^ { 2 } }$ 
A)  $\frac { 0 x + 12 } { 2 x }$ 
B)  $\frac { 0 x - 16 } { 2 x }$ 
C)  $\frac { 16 x - 16 } { 2 x }$ 
D)  $\frac { 0 x - 16 } { 2 x ^ { 2 } }$

Question 6

Perform the indicated operation. Simplify if possible.
-$\frac { 7 } { 13 + x } + \frac { x + 3 } { 13 + x }$

Accepted Answer

A)  $\frac { 10 } { 13 }$ 
B)  $\frac { x + 10 } { 26 + x }$ 
C)  $\frac { x + 10 } { 13 + x }$ 
D)  $\frac { 10 } { 26 }$ 
A)  $\frac { 10 } { 13 }$ 
B)  $\frac { x + 10 } { 26 + x }$ 
C)  $\frac { x + 10 } { 13 + x }$ 
D)  $\frac { 10 } { 26 }$

Question 7

Simplify.
-$\frac { \frac { 5 } { x } + \frac { 4 } { x ^ { 2 } } } { \frac { 25 } { x ^ { 2 } } - \frac { 16 } { x } }$

Accepted Answer

A)  $\frac { 5 x + 4 } { 25 - 16 x }$ 
B)  $\frac { 5 x ^ { 2 } + 4 } { 25 - 16 x }$ 
C)  $\frac { 1 } { 5 x - 4 }$ 
D)  $\frac { 1 } { 5 - 4 x }$ 
A)  $\frac { 5 x + 4 } { 25 - 16 x }$ 
B)  $\frac { 5 x ^ { 2 } + 4 } { 25 - 16 x }$ 
C)  $\frac { 1 } { 5 x - 4 }$ 
D)  $\frac { 1 } { 5 - 4 x }$

Question 8

Simplify.
-$\frac { 1 + \frac { 8 } { 15 } } { 3 + \frac { 7 } { 15 } }$

Accepted Answer

A)  $\frac { 23 } { 52 }$ 
B)  $\frac { 23 } { 45 }$ 
C)  $\frac { 1 } { 3 }$ 
D)  $\frac { 23 } { 15 }$ 
A)  $\frac { 23 } { 52 }$ 
B)  $\frac { 23 } { 45 }$ 
C)  $\frac { 1 } { 3 }$ 
D)  $\frac { 23 } { 15 }$

Question 9

Simplify the expression.
-$\frac { 6 x ^ { 3 } } { 3 x }$

Accepted Answer

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

Question 10

Solve the proportion.
-$\frac { 11 } { 6 } = \frac { x - 9 } { x - 5 }$

Accepted Answer

A)  $\frac { 69 } { 5 }$ 
B)  $- \frac { 4 } { 5 }$ 
C)  $\frac { 1 } { 5 }$ 
D)  $- \frac { 1 } { 5 }$ 
A)  $\frac { 69 } { 5 }$ 
B)  $- \frac { 4 } { 5 }$ 
C)  $\frac { 1 } { 5 }$ 
D)  $- \frac { 1 } { 5 }$

Question 11

Simplify.
-$\frac { \frac { 12 } { 13 - x } + \frac { 13 } { x - 13 } } { \frac { 6 } { x } + \frac { 7 } { x - 13 } }$

Accepted Answer

A)  $- \frac { x } { 13 x - 78 }$ 
B)  $- \frac { 25 x } { 13 x - 78 }$ 
C)  $\frac { 25 x } { 13 x - 78 }$ 
D)  $\frac { x } { 13 x - 78 }$ 
A)  $- \frac { x } { 13 x - 78 }$ 
B)  $- \frac { 25 x } { 13 x - 78 }$ 
C)  $\frac { 25 x } { 13 x - 78 }$ 
D)  $\frac { x } { 13 x - 78 }$

Question 12

Perform the indicated operation. Simplify if possible.
-$\frac { x ^ { 2 } + 14 } { x ^ { 2 } + 4 x - 12 } + \frac { 2 - 8 x } { 12 - 4 x - x ^ { 2 } }$

Accepted Answer

A)  $\frac { x + 2 } { x - 2 }$ 
B)  $\frac { x + 2 } { x ^ { 2 } + 4 x - 12 }$ 
C)  $\frac { x + 6 } { x - 2 }$ 
D)  $\frac { ( x - 6 ) ( x - 2 ) } { ( x + 6 ) ( x - 2 ) }$ 
A)  $\frac { x + 2 } { x - 2 }$ 
B)  $\frac { x + 2 } { x ^ { 2 } + 4 x - 12 }$ 
C)  $\frac { x + 6 } { x - 2 }$ 
D)  $\frac { ( x - 6 ) ( x - 2 ) } { ( x + 6 ) ( x - 2 ) }$

Question 13

Solve.
-A board of length $\frac { 2 } { x + 4 }$ inches was cut into two pieces. If one piece is $\frac { 5 } { x - 4 }$ inches, express the length of the other board as a rational expression.

Accepted Answer

A)  $\frac { - 3 } { ( x + 4 ) ( x - 4 ) }$ in. 
B)  $\frac { - 3 x + 12 } { ( x + 4 ) ( x - 4 ) }$ in. 
C)  $\frac { - 3 x - 28 } { ( x + 4 ) ( x - 4 ) } \mathrm { in }$. 
D)  $\frac { - 3 x + 28 } { ( x + 4 ) ( x - 4 ) }$ in. 
A)  $\frac { - 3 } { ( x + 4 ) ( x - 4 ) }$ in. 
B)  $\frac { - 3 x + 12 } { ( x + 4 ) ( x - 4 ) }$ in. 
C)  $\frac { - 3 x - 28 } { ( x + 4 ) ( x - 4 ) } \mathrm { in }$. 
D)  $\frac { - 3 x + 28 } { ( x + 4 ) ( x - 4 ) }$ in.

Question 14

Find the product and simplify.
-$\frac { 2 p - 2 } { p } \cdot \frac { 3 p ^ { 2 } } { 4 p - 4 }$

Accepted Answer

A)  $\frac { 2 } { 3 p }$ 
B)  $\frac { 6 p ^ { 3 } - 6 p ^ { 2 } } { 4 p ^ { 2 } - 4 p }$ 
C)  $\frac { 8 p ^ { 2 } + 16 p + 8 } { 3 p ^ { 3 } }$ 
D)  $\frac { 3 p } { 2 }$ 
A)  $\frac { 2 } { 3 p }$ 
B)  $\frac { 6 p ^ { 3 } - 6 p ^ { 2 } } { 4 p ^ { 2 } - 4 p }$ 
C)  $\frac { 8 p ^ { 2 } + 16 p + 8 } { 3 p ^ { 3 } }$ 
D)  $\frac { 3 p } { 2 }$

Question 15

Find the product and simplify.
-$\frac { 9 x ^ { 4 } - 72 x } { 3 x ^ { 2 } - 12 } \cdot \frac { x ^ { 2 } + x - 2 } { 4 x ^ { 3 } + 8 x ^ { 2 } + 16 x }$

Accepted Answer

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

Question 16

Given that the pair of triangles is similar, find the missing length.
-

Accepted Answer

A)  $x = 28$ 
B)  $x = 7$ 
C)  $x = 21$ 
D)  $x = 12$ 
A)  $x = 28$ 
B)  $x = 7$ 
C)  $x = 21$ 
D)  $x = 12$

Question 17

Perform the indicated operation. Simplify if possible.
-$- \frac { 8 } { 49 } - \frac { 9 } { 7 x }$

Accepted Answer

A)  $\frac { - 8 x + 63 } { 49 x }$ 
B)  $\frac { 8 x - 63 } { 49 x }$ 
C)  $\frac { - 17 } { 49 - 7 x }$ 
D)  $\frac { - 8 x - 63 } { 49 x }$ 
A)  $\frac { - 8 x + 63 } { 49 x }$ 
B)  $\frac { 8 x - 63 } { 49 x }$ 
C)  $\frac { - 17 } { 49 - 7 x }$ 
D)  $\frac { - 8 x - 63 } { 49 x }$

Question 18

Solve the equation.
-$\frac { 4 } { y } + 7 = 5$

Accepted Answer

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

Question 19

Perform the indicated operation. Simplify if possible.
-$\frac { x ^ { 3 } + 1 } { x ^ { 3 } - x ^ { 2 } + x } \cdot \frac { 12 x } { - 72 x - 72 }$

Accepted Answer

A)  $\frac { x + 1 } { 6 ( - x - 1 ) }$ 
B)  $- \frac { 1 } { 6 }$ 
C)  $- \frac { x ^ { 3 } + 1 } { 6 ( x + 1 ) }$ 
D)  $- \frac { x ^ { 2 } + 1 } { 6 }$ 
A)  $\frac { x + 1 } { 6 ( - x - 1 ) }$ 
B)  $- \frac { 1 } { 6 }$ 
C)  $- \frac { x ^ { 3 } + 1 } { 6 ( x + 1 ) }$ 
D)  $- \frac { x ^ { 2 } + 1 } { 6 }$

Question 20

Rewrite the rational expression as an equivalent rational expression with the given denominator.
-

Accepted Answer

A)  $\frac { a ^ { 2 } - b ^ { 2 } } { a ^ { 2 } - 4 b ^ { 2 } }$ 
B)  $\frac { 2 a b } { a ^ { 2 } - 4 b ^ { 2 } }$ 
C)  $\frac { a } { a ^ { 2 } - 4 b ^ { 2 } }$ 
D)  $\frac { a ^ { 2 } - 2 a b } { a ^ { 2 } - 4 b ^ { 2 } }$ 
A)  $\frac { a ^ { 2 } - b ^ { 2 } } { a ^ { 2 } - 4 b ^ { 2 } }$ 
B)  $\frac { 2 a b } { a ^ { 2 } - 4 b ^ { 2 } }$ 
C)  $\frac { a } { a ^ { 2 } - 4 b ^ { 2 } }$ 
D)  $\frac { a ^ { 2 } - 2 a b } { a ^ { 2 } - 4 b ^ { 2 } }$

Find the quotient and simplify. - $\frac { z ^ { 2 } + 8 z + 16 } { z ^ { 2 } + 11 z + 28 } \div \frac { z ^ { 2 } + 4 z } { z ^ { 2 } + 17 z + 70 }$

Solve the problem. -If $f ( x ) = \frac { x ^ { 2 } - 2 } { x ^ { 3 } + 3 x }$ , find $f ( 2 )$

Simplify. - $\frac { \frac { x } { 8 } } { \frac { 3 } { x + 7 } }$

Perform the indicated operation. Simplify if possible. - $\frac { x } { 14 } + \frac { 13 } { 14 }$

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

Perform the indicated operation. Simplify if possible. - $\frac { 7 } { 13 + x } + \frac { x + 3 } { 13 + x }$

Simplify. - $\frac { \frac { 5 } { x } + \frac { 4 } { x ^ { 2 } } } { \frac { 25 } { x ^ { 2 } } - \frac { 16 } { x } }$

Simplify. - $\frac { 1 + \frac { 8 } { 15 } } { 3 + \frac { 7 } { 15 } }$

Simplify the expression. - $\frac { 6 x ^ { 3 } } { 3 x }$

Solve the proportion. - $\frac { 11 } { 6 } = \frac { x - 9 } { x - 5 }$

Simplify. - $\frac { \frac { 12 } { 13 - x } + \frac { 13 } { x - 13 } } { \frac { 6 } { x } + \frac { 7 } { x - 13 } }$

Perform the indicated operation. Simplify if possible. - $\frac { x ^ { 2 } + 14 } { x ^ { 2 } + 4 x - 12 } + \frac { 2 - 8 x } { 12 - 4 x - x ^ { 2 } }$

Solve. -A board of length $\frac { 2 } { x + 4 }$ inches was cut into two pieces. If one piece is $\frac { 5 } { x - 4 }$ inches, express the length of the other board as a rational expression.

Find the product and simplify. - $\frac { 2 p - 2 } { p } \cdot \frac { 3 p ^ { 2 } } { 4 p - 4 }$

Find the product and simplify. - $\frac { 9 x ^ { 4 } - 72 x } { 3 x ^ { 2 } - 12 } \cdot \frac { x ^ { 2 } + x - 2 } { 4 x ^ { 3 } + 8 x ^ { 2 } + 16 x }$

Given that the pair of triangles is similar, find the missing length. -

Perform the indicated operation. Simplify if possible. - $- \frac { 8 } { 49 } - \frac { 9 } { 7 x }$

Solve the equation. - $\frac { 4 } { y } + 7 = 5$

Perform the indicated operation. Simplify if possible. - $\frac { x ^ { 3 } + 1 } { x ^ { 3 } - x ^ { 2 } + x } \cdot \frac { 12 x } { - 72 x - 72 }$

Rewrite the rational expression as an equivalent rational expression with the given denominator. -

Review of Real Numbers

Equations, Inequalities, and Problem Solving

Graphing

Solving Systems of Linear Equations

Exponents and Polynomials

Factoring Polynomials

More on Functions and Graphs

Inequalities and Absolute Value

Rational Exponents, Radicals, and Complex Numbers

Quadratic Equations and Functions

Exponential and Logarithmic Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Exam 7: Rational Expressions

Find the quotient and simplify. - z2+8z+16z2+11z+28÷z2+4zz2+17z+70\frac { z ^ { 2 } + 8 z + 16 } { z ^ { 2 } + 11 z + 28 } \div \frac { z ^ { 2 } + 4 z } { z ^ { 2 } + 17 z + 70 }z2+11z+28z2+8z+16​÷z2+17z+70z2+4z​

Solve the problem. -If f(x)=x2−2x3+3xf ( x ) = \frac { x ^ { 2 } - 2 } { x ^ { 3 } + 3 x }f(x)=x3+3xx2−2​ , find f(2)f ( 2 )f(2)

Simplify. - x83x+7\frac { \frac { x } { 8 } } { \frac { 3 } { x + 7 } }x+73​8x​​

Perform the indicated operation. Simplify if possible. - x14+1314\frac { x } { 14 } + \frac { 13 } { 14 }14x​+1413​

Perform the indicated operation. Simplify if possible. - 4x−7x+−8x−22x\frac { 4 x - 7 } { x } + \frac { - 8 x - 2 } { 2 x }x4x−7​+2x−8x−2​

Perform the indicated operation. Simplify if possible. - 713+x+x+313+x\frac { 7 } { 13 + x } + \frac { x + 3 } { 13 + x }13+x7​+13+xx+3​

Simplify. - 5x+4x225x2−16x\frac { \frac { 5 } { x } + \frac { 4 } { x ^ { 2 } } } { \frac { 25 } { x ^ { 2 } } - \frac { 16 } { x } }x225​−x16​x5​+x24​​

Simplify. - 1+8153+715\frac { 1 + \frac { 8 } { 15 } } { 3 + \frac { 7 } { 15 } }3+157​1+158​​

Simplify the expression. - 6x33x\frac { 6 x ^ { 3 } } { 3 x }3x6x3​

Solve the proportion. - 116=x−9x−5\frac { 11 } { 6 } = \frac { x - 9 } { x - 5 }611​=x−5x−9​

Simplify. - 1213−x+13x−136x+7x−13\frac { \frac { 12 } { 13 - x } + \frac { 13 } { x - 13 } } { \frac { 6 } { x } + \frac { 7 } { x - 13 } }x6​+x−137​13−x12​+x−1313​​

Perform the indicated operation. Simplify if possible. - x2+14x2+4x−12+2−8x12−4x−x2\frac { x ^ { 2 } + 14 } { x ^ { 2 } + 4 x - 12 } + \frac { 2 - 8 x } { 12 - 4 x - x ^ { 2 } }x2+4x−12x2+14​+12−4x−x22−8x​

Solve. -A board of length 2x+4\frac { 2 } { x + 4 }x+42​ inches was cut into two pieces. If one piece is 5x−4\frac { 5 } { x - 4 }x−45​ inches, express the length of the other board as a rational expression.

Find the product and simplify. - 2p−2p⋅3p24p−4\frac { 2 p - 2 } { p } \cdot \frac { 3 p ^ { 2 } } { 4 p - 4 }p2p−2​⋅4p−43p2​

Find the product and simplify. - 9x4−72x3x2−12⋅x2+x−24x3+8x2+16x\frac { 9 x ^ { 4 } - 72 x } { 3 x ^ { 2 } - 12 } \cdot \frac { x ^ { 2 } + x - 2 } { 4 x ^ { 3 } + 8 x ^ { 2 } + 16 x }3x2−129x4−72x​⋅4x3+8x2+16xx2+x−2​