Question 1

Perform the indicated operation. Simplify if possible.
-$\frac { 5 x } { 13 } + \frac { 3 x } { 13 }$

Accepted Answer

A)  $\frac { 13 } { 8 x }$ 
B)  $8 \mathrm { x }$ 
C)  $\frac { 8 x } { 13 }$ 
D)  $\frac { 8 \mathrm { x } } { 26 }$ 
A)  $\frac { 13 } { 8 x }$ 
B)  $8 \mathrm { x }$ 
C)  $\frac { 8 x } { 13 }$ 
D)  $\frac { 8 \mathrm { x } } { 26 }$

Question 2

Perform the indicated operation. Simplify if possible.
-$\frac { x + 2 } { x ^ { 2 } + 13 x + 42 } + \frac { 5 x + 3 } { x ^ { 2 } + 10 x + 24 }$

Accepted Answer

A)  $\frac { 6 x ^ { 2 } + 44 x + 29 } { ( x - 6 ) ( x - 7 ) ( x - 4 ) }$ 
B)  $\frac { 6 x + 5 } { 2 x ^ { 2 } + 23 x + 66 }$ 
C)  $6 x + 5$ 
D)  $\frac { 6 x ^ { 2 } + 44 x + 29 } { ( x + 6 ) ( x + 7 ) ( x + 4 ) }$ 
A)  $\frac { 6 x ^ { 2 } + 44 x + 29 } { ( x - 6 ) ( x - 7 ) ( x - 4 ) }$ 
B)  $\frac { 6 x + 5 } { 2 x ^ { 2 } + 23 x + 66 }$ 
C)  $6 x + 5$ 
D)  $\frac { 6 x ^ { 2 } + 44 x + 29 } { ( x + 6 ) ( x + 7 ) ( x + 4 ) }$

Question 3

Simplify the rational expression.
-$\frac { 5 x - 20 } { 2 x - 8 }$

Accepted Answer

A)  4 
B)  $- \frac { 5 } { 2 }$ 
C)  $\frac { 5 } { 2 }$ 
D)  $- 4$ 
A)  4 
B)  $- \frac { 5 } { 2 }$ 
C)  $\frac { 5 } { 2 }$ 
D)  $- 4$

Question 4

Simplify the rational expression.
-$\frac { 4 x + 3 } { 20 x ^ { 2 } + 27 x + 9 }$

Accepted Answer

A)  $\frac { 4 x + 5 } { 5 x + 27 }$ 
B)  $\frac { 4 x + 3 } { 20 x ^ { 2 } + 27 x + 9 }$ 
C)  $\frac { 4 x } { 5 x + 3 }$ 
D)  $\frac { 1 } { 5 x + 3 }$ 
A)  $\frac { 4 x + 5 } { 5 x + 27 }$ 
B)  $\frac { 4 x + 3 } { 20 x ^ { 2 } + 27 x + 9 }$ 
C)  $\frac { 4 x } { 5 x + 3 }$ 
D)  $\frac { 1 } { 5 x + 3 }$

Question 5

Simplify.
-$\frac { 1 + \frac { 9 } { 16 } } { 3 + \frac { 7 } { 16 } }$

Accepted Answer

A)  $\frac { 25 } { 48 }$ 
B)  $\frac { 5 } { 11 }$ 
C)  $\frac { 5 } { 16 }$ 
D)  $\frac { 25 } { 16 }$ 
A)  $\frac { 25 } { 48 }$ 
B)  $\frac { 5 } { 11 }$ 
C)  $\frac { 5 } { 16 }$ 
D)  $\frac { 25 } { 16 }$

Question 6

Find the product and simplify.
-$\frac { y ^ { 2 } - w ^ { 2 } } { y + w } \cdot \frac { y } { y ^ { 2 } - y w }$

Accepted Answer

A)  $y$ 
B)  1 
C)  $- \mathrm { y }$ 
D)  $- \frac { 1 } { y }$ 
A)  $y$ 
B)  1 
C)  $- \mathrm { y }$ 
D)  $- \frac { 1 } { y }$

Question 7

Solve the equation.
-$\frac { x } { 2 } + \frac { 7 x } { 3 } = \frac { x } { 6 }$

Accepted Answer

A)  0 
B)  42 
C)  6 
D)  21 
A)  0 
B)  42 
C)  6 
D)  21

Question 8

Solve the equation.
-$\frac { 1 } { x + 7 } + \frac { 5 } { x + 6 } = \frac { - 1 } { x ^ { 2 } + 13 x + 42 }$

Accepted Answer

A)  0 
B)  6 
C)  $- 7$ 
D)  no solution 
A)  0 
B)  6 
C)  $- 7$ 
D)  no solution

Question 9

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

Accepted Answer

A)  $x = 0.72$ 
B)  $x = 7.2$ 
C)  $x = 450$ 
D)  $x = 45$ 
A)  $x = 0.72$ 
B)  $x = 7.2$ 
C)  $x = 450$ 
D)  $x = 45$

Question 10

Simplify.
-$\frac { \frac { x } { 4 } - \frac { 1 } { x } } { 1 + \frac { 2 } { x } }$

Accepted Answer

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

Question 11

Simplify.
-$\frac { \frac { 64 s ^ { 2 } - 9 r ^ { 2 } } { r s } } { \frac { 8 } { r } - \frac { 3 } { s } }$

Accepted Answer

A)  $8 r + 3 s$ 
B)  $\frac { r s } { 8 r + 3 s }$ 
C)  $\frac { 3 r + 8 s } { r s }$ 
D)  $3 r + 8 s$ 
A)  $8 r + 3 s$ 
B)  $\frac { r s } { 8 r + 3 s }$ 
C)  $\frac { 3 r + 8 s } { r s }$ 
D)  $3 r + 8 s$

Question 12

Find the product and simplify.
-$\frac { 6 } { x + 6 } \cdot \frac { x } { 7 }$

Accepted Answer

A)  $\frac { 6 x } { 7 ( x + 6 ) }$ 
B)  $\frac { x } { ( x + 7 ) }$ 
C)  $\frac { 1 } { 7 }$ 
D)  $\frac { 6 } { 7 }$ 
A)  $\frac { 6 x } { 7 ( x + 6 ) }$ 
B)  $\frac { x } { ( x + 7 ) }$ 
C)  $\frac { 1 } { 7 }$ 
D)  $\frac { 6 } { 7 }$

Question 13

Solve.
-A boat moves 8 kilometers upstream in the same amount of time it moves 20 kilometers downstream. If the rate of the current is 8 kilometers per hour, find the rate of the boat in still water.

Accepted Answer

A)  $13 \frac { 1 } { 3 } \mathrm {~km} / \mathrm { hr }$ 
B)  $5 \frac { 1 } { 3 } \mathrm {~km} / \mathrm { hr }$ 
C)  $8 \mathrm {~km} / \mathrm { hr }$ 
D)  $18 \frac { 2 } { 3 } \mathrm {~km} / \mathrm { hr }$ 
A)  $13 \frac { 1 } { 3 } \mathrm {~km} / \mathrm { hr }$ 
B)  $5 \frac { 1 } { 3 } \mathrm {~km} / \mathrm { hr }$ 
C)  $8 \mathrm {~km} / \mathrm { hr }$ 
D)  $18 \frac { 2 } { 3 } \mathrm {~km} / \mathrm { hr }$

Question 14

Find the quotient and simplify.
-$\frac { m ^ { 2 } - n ^ { 2 } } { m - n } \div \frac { m } { m ^ { 2 } + m n }$

Accepted Answer

A)  $( m + n )$ 
B)  $( \mathrm { m } + \mathrm { n } ) ^ { 2 }$ 
C)  $( \mathrm { m } - \mathrm { n } ) ^ { 2 }$ 
D)  $( \mathrm { m } - \mathrm { n } ) ( \mathrm { m } + \mathrm { n } )$ 
A)  $( m + n )$ 
B)  $( \mathrm { m } + \mathrm { n } ) ^ { 2 }$ 
C)  $( \mathrm { m } - \mathrm { n } ) ^ { 2 }$ 
D)  $( \mathrm { m } - \mathrm { n } ) ( \mathrm { m } + \mathrm { n } )$

Question 15

Solve the equation for the indicated variable.
-$T = \frac { V } { Q } \quad \text { for } Q$

Accepted Answer

A)  $Q = V + T$ 
B)  $Q = \frac { T } { V }$ 
C)  $Q = V T$ 
D)  $Q = \frac { V } { T }$ 
A)  $Q = V + T$ 
B)  $Q = \frac { T } { V }$ 
C)  $Q = V T$ 
D)  $Q = \frac { V } { T }$

Question 16

Fill in the blank with one of the words or phrases listed below. Not all choices will be used. $$\begin{array} { l l l l } 
\text { least common denominator } & \text { simplifying } & \text { reciprocals } & \text { numerator } \
\text { cross products } & \text { ratio } & \text { proportion } & \text { denominator } \
\text { rational expression } & \text { domain } & \text { complex fraction } & \
\frac { - a } { b } & \frac { a } { - b } & \frac { - a } { - b } &
\end{array}$$
-If $\frac { \mathrm { a } } { \mathrm { b } } = \frac { \mathrm { c } } { \mathrm { d } }$, then ad and bc are called______

Accepted Answer

A)  least common denominator 
B)  cross products 
C)  complex fraction 
D)  reciprocals 
A)  least common denominator 
B)  cross products 
C)  complex fraction 
D)  reciprocals

Question 17

Solve the equation.
-$\frac { 3 } { a - 3 } = \frac { a } { a - 3 } - 5$

Accepted Answer

A)  3 
B)  no solution 
C)  $- 3$ 
D)  $3 , - 3$ 
A)  3 
B)  no solution 
C)  $- 3$ 
D)  $3 , - 3$

Question 18

Simplify the rational expression.
-$\frac { x + 5 } { x ^ { 3 } + 125 }$

Accepted Answer

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

Question 19

Perform the indicated operation. Simplify if possible.
-$\frac { x } { x ^ { 2 } - 121 } - \frac { 11 } { 121 - x ^ { 2 } }$

Accepted Answer

A)  $- \frac { 1 } { x - 11 }$ 
B)  $\frac { 1 } { x - 11 }$ 
C)  $\frac { 1 } { x + 11 }$ 
D)  $- \frac { 1 } { x + 11 }$ 
A)  $- \frac { 1 } { x - 11 }$ 
B)  $\frac { 1 } { x - 11 }$ 
C)  $\frac { 1 } { x + 11 }$ 
D)  $- \frac { 1 } { x + 11 }$

Question 20

Simplify.
-$\frac { m ^ { - 1 } + z ^ { - 1 } } { m ^ { - 1 } - z ^ { - 1 } }$

Accepted Answer

A)  $\frac { z + m } { z }$ 
B)  $\frac { \mathrm { z } + \mathrm { m } } { \mathrm { m } }$ 
C)  $\frac { z - m } { z }$ 
D)  $\frac { \mathrm { z } + \mathrm { m } } { \mathrm { z } - \mathrm { m } }$ 
A)  $\frac { z + m } { z }$ 
B)  $\frac { \mathrm { z } + \mathrm { m } } { \mathrm { m } }$ 
C)  $\frac { z - m } { z }$ 
D)  $\frac { \mathrm { z } + \mathrm { m } } { \mathrm { z } - \mathrm { m } }$

Perform the indicated operation. Simplify if possible. - $\frac { 5 x } { 13 } + \frac { 3 x } { 13 }$

Perform the indicated operation. Simplify if possible. - $\frac { x + 2 } { x ^ { 2 } + 13 x + 42 } + \frac { 5 x + 3 } { x ^ { 2 } + 10 x + 24 }$

Simplify the rational expression. - $\frac { 5 x - 20 } { 2 x - 8 }$

Simplify the rational expression. - $\frac { 4 x + 3 } { 20 x ^ { 2 } + 27 x + 9 }$

Simplify. - $\frac { 1 + \frac { 9 } { 16 } } { 3 + \frac { 7 } { 16 } }$

Find the product and simplify. - $\frac { y ^ { 2 } - w ^ { 2 } } { y + w } \cdot \frac { y } { y ^ { 2 } - y w }$

Solve the equation. - $\frac { x } { 2 } + \frac { 7 x } { 3 } = \frac { x } { 6 }$

Solve the equation. - $\frac { 1 } { x + 7 } + \frac { 5 } { x + 6 } = \frac { - 1 } { x ^ { 2 } + 13 x + 42 }$

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

Simplify. - $\frac { \frac { x } { 4 } - \frac { 1 } { x } } { 1 + \frac { 2 } { x } }$

Simplify. - $\frac { \frac { 64 s ^ { 2 } - 9 r ^ { 2 } } { r s } } { \frac { 8 } { r } - \frac { 3 } { s } }$

Find the product and simplify. - $\frac { 6 } { x + 6 } \cdot \frac { x } { 7 }$

Solve. -A boat moves 8 kilometers upstream in the same amount of time it moves 20 kilometers downstream. If the rate of the current is 8 kilometers per hour, find the rate of the boat in still water.

Find the quotient and simplify. - $\frac { m ^ { 2 } - n ^ { 2 } } { m - n } \div \frac { m } { m ^ { 2 } + m n }$

Solve the equation for the indicated variable. - $T = \frac { V } { Q } \quad \text { for } Q$

Solve the equation. - $\frac { 3 } { a - 3 } = \frac { a } { a - 3 } - 5$

Simplify the rational expression. - $\frac { x + 5 } { x ^ { 3 } + 125 }$

Perform the indicated operation. Simplify if possible. - $\frac { x } { x ^ { 2 } - 121 } - \frac { 11 } { 121 - x ^ { 2 } }$

Simplify. - $\frac { m ^ { - 1 } + z ^ { - 1 } } { m ^ { - 1 } - z ^ { - 1 } }$

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

Perform the indicated operation. Simplify if possible. - 5x13+3x13\frac { 5 x } { 13 } + \frac { 3 x } { 13 }135x​+133x​

Perform the indicated operation. Simplify if possible. - x+2x2+13x+42+5x+3x2+10x+24\frac { x + 2 } { x ^ { 2 } + 13 x + 42 } + \frac { 5 x + 3 } { x ^ { 2 } + 10 x + 24 }x2+13x+42x+2​+x2+10x+245x+3​

Simplify the rational expression. - 5x−202x−8\frac { 5 x - 20 } { 2 x - 8 }2x−85x−20​

Simplify the rational expression. - 4x+320x2+27x+9\frac { 4 x + 3 } { 20 x ^ { 2 } + 27 x + 9 }20x2+27x+94x+3​

Simplify. - 1+9163+716\frac { 1 + \frac { 9 } { 16 } } { 3 + \frac { 7 } { 16 } }3+167​1+169​​

Find the product and simplify. - y2−w2y+w⋅yy2−yw\frac { y ^ { 2 } - w ^ { 2 } } { y + w } \cdot \frac { y } { y ^ { 2 } - y w }y+wy2−w2​⋅y2−ywy​

Solve the equation. - x2+7x3=x6\frac { x } { 2 } + \frac { 7 x } { 3 } = \frac { x } { 6 }2x​+37x​=6x​

Solve the equation. - 1x+7+5x+6=−1x2+13x+42\frac { 1 } { x + 7 } + \frac { 5 } { x + 6 } = \frac { - 1 } { x ^ { 2 } + 13 x + 42 }x+71​+x+65​=x2+13x+42−1​