Question 1

Simplify.
-$\frac { \frac { 2 } { x } + \frac { 3 } { x ^ { 2 } } } { \frac { 4 } { x ^ { 2 } } - \frac { 9 } { x } }$

Accepted Answer

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

Question 2

Perform the indicated operation. Simplify if possible.
-$\frac { 5 m } { m - 6 } - \frac { 30 } { m - 6 }$

Accepted Answer

A)  $\frac { 5 ( m + 6 ) } { m - 6 }$ 
B)  0 
C)  $\frac { 5 } { m - 6 }$ 
D)  5 
A)  $\frac { 5 ( m + 6 ) } { m - 6 }$ 
B)  0 
C)  $\frac { 5 } { m - 6 }$ 
D)  5 D

Question 3

Solve the proportion.
-$\frac { 9 } { 8 } = \frac { 2 x } { 7 }$

Accepted Answer

A)  $\frac { 8 } { 5 }$ 
B)  $\frac { 63 } { 8 }$ 
C)  $\frac { 63 } { 16 }$ 
D)  $\frac { 28 } { 9 }$ 
A)  $\frac { 8 } { 5 }$ 
B)  $\frac { 63 } { 8 }$ 
C)  $\frac { 63 } { 16 }$ 
D)  $\frac { 28 } { 9 }$ C

Question 4

Solve.
-On an architect's blueprint, 1 inch corresponds to 4 feet. If an exterior wall is 12 feet long, find how long the blueprint measurement should be. Write answer as a mixed number if necessary.

Accepted Answer

A)  $12 \mathrm { in }$. 
B)  $3 \frac { 1 } { 3 } \mathrm { in }$. 
C)  $4 \mathrm { in }$. 
D)  $3 \mathrm { in }$. 
A)  $12 \mathrm { in }$. 
B)  $3 \frac { 1 } { 3 } \mathrm { in }$. 
C)  $4 \mathrm { in }$. 
D)  $3 \mathrm { in }$.

Question 5

Perform the indicated operation. Simplify if possible.
-$\frac { 2 } { x + 2 } + \frac { 3 } { 9 x + 18 }$

Accepted Answer

A)  $\frac { 29 } { 9 ( x + 2 ) }$ 
B)  $\frac { 7 } { 3 ( x + 2 ) }$ 
C)  $\frac { 5 } { 9 ( x + 2 ) }$ 
D)  $\frac { 7 } { 3 ( x + 2 ) ^ { 2 } }$ 
A)  $\frac { 29 } { 9 ( x + 2 ) }$ 
B)  $\frac { 7 } { 3 ( x + 2 ) }$ 
C)  $\frac { 5 } { 9 ( x + 2 ) }$ 
D)  $\frac { 7 } { 3 ( x + 2 ) ^ { 2 } }$

Question 6

Rewrite the rational expression as an equivalent rational expression with the given denominator.
-$\frac { 6 } { x ^ { 2 } + 9 x } = \frac { } { x ( x + 9 ) ( x + 4 ) }$

Accepted Answer

A)  $\frac { 6 ( x + 9 ) } { x ( x + 9 ) ( x + 4 ) }$ 
B)  $\frac { 6 ( x - 4 ) } { x ( x + 9 ) ( x + 4 ) }$ 
C)  $\frac { 6 } { x ( x + 9 ) ( x + 4 ) }$ 
D)  $\frac { 6 ( x + 4 ) } { x ( x + 9 ) ( x + 4 ) }$ 
A)  $\frac { 6 ( x + 9 ) } { x ( x + 9 ) ( x + 4 ) }$ 
B)  $\frac { 6 ( x - 4 ) } { x ( x + 9 ) ( x + 4 ) }$ 
C)  $\frac { 6 } { x ( x + 9 ) ( x + 4 ) }$ 
D)  $\frac { 6 ( x + 4 ) } { x ( x + 9 ) ( x + 4 ) }$

Question 7

Simplify.
-$\frac { \frac { 10 } { a } + 10 } { \frac { 10 } { a } - 10 }$

Accepted Answer

A)  $10 - a ^ { 2 }$ 
B)  $\frac { 1 + a } { 1 - a }$ 
C)  $\frac { 10 ( 1 + a ) } { 1 - a }$ 
D)  $\frac { a ^ { 2 } } { 10 - a ^ { 2 } }$ 
A)  $10 - a ^ { 2 }$ 
B)  $\frac { 1 + a } { 1 - a }$ 
C)  $\frac { 10 ( 1 + a ) } { 1 - a }$ 
D)  $\frac { a ^ { 2 } } { 10 - a ^ { 2 } }$

Question 8

Solve the equation.
-$\frac { 5 x } { 7 } - 3 = x$

Accepted Answer

A)  $\frac { 2 } { 7 }$ 
B)  $\frac { 2 } { 21 }$ 
C)  $- \frac { 21 } { 2 }$ 
D)  $\frac { 7 } { 5 }$ 
A)  $\frac { 2 } { 7 }$ 
B)  $\frac { 2 } { 21 }$ 
C)  $- \frac { 21 } { 2 }$ 
D)  $\frac { 7 } { 5 }$

Question 9

Solve.
-A punch recipe calls for mixing 2 parts of orange juice with 7 parts of lemon juice. Find how much orange juice should be mixed with 56 ounces of lemon juice.

Accepted Answer

A)  $16 \mathrm { oz }$ 
B)  $8 \mathrm { oz }$ 
C)  $196 \mathrm { oz }$ 
D)  $28 \mathrm { oz }$ 
A)  $16 \mathrm { oz }$ 
B)  $8 \mathrm { oz }$ 
C)  $196 \mathrm { oz }$ 
D)  $28 \mathrm { oz }$

Question 10

Perform the indicated operation. Simplify if possible.
-$\frac { 11 } { 2 x - 11 } - \frac { 17 } { 11 - 2 x }$

Accepted Answer

A)  $\frac { 6 } { 2 x - 11 }$ 
B)  $- \frac { 6 } { 2 x - 11 }$ 
C)  $- \frac { 28 } { 2 x - 11 }$ 
D)  $\frac { 28 } { 2 x - 11 }$ 
A)  $\frac { 6 } { 2 x - 11 }$ 
B)  $- \frac { 6 } { 2 x - 11 }$ 
C)  $- \frac { 28 } { 2 x - 11 }$ 
D)  $\frac { 28 } { 2 x - 11 }$

Question 11

Perform the indicated operation. Simplify if possible.
-$\frac { 5 a + 4 b } { 2 } - \frac { 5 a - 4 b } { 2 }$

Accepted Answer

A)  $16 b$ 
B)  $4 \mathrm {~b}$ 
C)  0 
D)  $5 a$ 
A)  $16 b$ 
B)  $4 \mathrm {~b}$ 
C)  0 
D)  $5 a$

Question 12

Perform the indicated operation. Simplify if possible.
-$\frac { x + 4 } { 9 } + \frac { 3 } { 9 }$

Accepted Answer

A)  $\frac { x + 7 } { 9 }$ 
B)  $\frac { x + 7 } { 18 }$ 
C)  $\frac { 7 x } { 18 }$ 
D)  $\frac { 7 \mathrm { x } } { 9 }$ 
A)  $\frac { x + 7 } { 9 }$ 
B)  $\frac { x + 7 } { 18 }$ 
C)  $\frac { 7 x } { 18 }$ 
D)  $\frac { 7 \mathrm { x } } { 9 }$

Question 13

Solve the proportion.
-$\frac { x + 5 } { x } = \frac { 2 } { 3 }$

Accepted Answer

A)  - 5 
B)  - 15 
C)  10 
D)  3 
A)  - 5 
B)  - 15 
C)  10 
D)  3

Question 14

Convert as indicated.
-1152 square inches=_____ square feet

Accepted Answer

A)  13,824 
B)  8 
C)  96 
D)  165,888 
A)  13,824 
B)  8 
C)  96 
D)  165,888

Question 15

Find the domain of the rational function.
-$g ( x ) = \frac { x ^ { 2 } - 25 } { x ^ { 2 } - 15 x + 54 }$

Accepted Answer

A)  $\{ x \mid x$ is a real number and $x \neq 5 , x \neq - 5 \}$ 
B)  $\{ x \mid x$ is a real number and $x \neq - 6 , x \neq - 9 \}$ 
C)  $\{ x \mid x$ is a real number and $x \neq 0 \}$ 
D)  $\{ x \mid x$ is a real number and $x \neq 6 , x \neq 9 \}$ 
A)  $\{ x \mid x$ is a real number and $x \neq 5 , x \neq - 5 \}$ 
B)  $\{ x \mid x$ is a real number and $x \neq - 6 , x \neq - 9 \}$ 
C)  $\{ x \mid x$ is a real number and $x \neq 0 \}$ 
D)  $\{ x \mid x$ is a real number and $x \neq 6 , x \neq 9 \}$

Question 16

Perform the indicated operations. Simplify if possible.
-$\frac { 3 x } { x + 1 } + \frac { 4 } { x - 1 } - \frac { 6 } { x ^ { 2 } - 1 }$

Accepted Answer

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

Question 17

Solve.
-One number plus eighteen times its reciprocal is equal to nine.

Accepted Answer

A)  $- 3$ or 6 
B)  $- 6$ or 3 
C)  $- 6$ or $- 3$ 
D)  3 or 6 
A)  $- 3$ or 6 
B)  $- 6$ or 3 
C)  $- 6$ or $- 3$ 
D)  3 or 6

Question 18

Find the quotient and simplify.
-$\frac { 35 m ^ { 2 } - 57 m n + 18 n ^ { 2 } } { 35 m ^ { 2 } - 43 m n + 12 n ^ { 2 } } \div \frac { 35 m ^ { 2 } - 12 m n - 36 n ^ { 2 } } { 49 m ^ { 2 } + 98 m n + 48 n ^ { 2 } }$

Accepted Answer

A)  $\frac { ( 5 m + 6 n ) ^ { 2 } } { ( 7 m - 8 n ) ( 5 m + 4 n ) }$ 
B)  $\frac { ( 5 m + 4 n ) } { ( 7 m - 8 n ) }$ 
C)  $\frac { ( 5 m - 6 n ) ^ { 2 } } { ( 7 m + 8 n ) ( 5 m - 4 n ) }$ 
D)  $\frac { 7 m + 8 n } { 5 m - 4 n }$ 
A)  $\frac { ( 5 m + 6 n ) ^ { 2 } } { ( 7 m - 8 n ) ( 5 m + 4 n ) }$ 
B)  $\frac { ( 5 m + 4 n ) } { ( 7 m - 8 n ) }$ 
C)  $\frac { ( 5 m - 6 n ) ^ { 2 } } { ( 7 m + 8 n ) ( 5 m - 4 n ) }$ 
D)  $\frac { 7 m + 8 n } { 5 m - 4 n }$

Question 19

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

Accepted Answer

A)  $x = 10$ 
B)  $x = 14$ 
C)  $x = 7$ 
D)  $x = 21$ 
A)  $x = 10$ 
B)  $x = 14$ 
C)  $x = 7$ 
D)  $x = 21$

Question 20

Perform the indicated operation. Simplify if possible.
-$\frac { x } { x ^ { 2 } - 16 } - \frac { 5 } { x ^ { 2 } + 5 x + 4 }$

Accepted Answer

A)  $\frac { x ^ { 2 } - 4 } { ( x - 4 ) ( x + 4 ) ( x + 1 ) }$ 
B)  $\frac { x ^ { 2 } - 4 x + 20 } { ( x - 4 ) ( x + 4 ) }$ 
C)  $\frac { x ^ { 2 } - 4 x + 20 } { ( x - 4 ) ( x + 4 ) ( x + 1 ) }$ 
D)  $\frac { x ^ { 2 } + 4 x + 20 } { ( x - 4 ) ( x + 4 ) ( x + 1 ) }$ 
A)  $\frac { x ^ { 2 } - 4 } { ( x - 4 ) ( x + 4 ) ( x + 1 ) }$ 
B)  $\frac { x ^ { 2 } - 4 x + 20 } { ( x - 4 ) ( x + 4 ) }$ 
C)  $\frac { x ^ { 2 } - 4 x + 20 } { ( x - 4 ) ( x + 4 ) ( x + 1 ) }$ 
D)  $\frac { x ^ { 2 } + 4 x + 20 } { ( x - 4 ) ( x + 4 ) ( x + 1 ) }$

Simplify. - $\frac { \frac { 2 } { x } + \frac { 3 } { x ^ { 2 } } } { \frac { 4 } { x ^ { 2 } } - \frac { 9 } { x } }$

Perform the indicated operation. Simplify if possible. - $\frac { 5 m } { m - 6 } - \frac { 30 } { m - 6 }$

Solve the proportion. - $\frac { 9 } { 8 } = \frac { 2 x } { 7 }$

Solve. -On an architect's blueprint, 1 inch corresponds to 4 feet. If an exterior wall is 12 feet long, find how long the blueprint measurement should be. Write answer as a mixed number if necessary.

Perform the indicated operation. Simplify if possible. - $\frac { 2 } { x + 2 } + \frac { 3 } { 9 x + 18 }$

Rewrite the rational expression as an equivalent rational expression with the given denominator. - $\frac { 6 } { x ^ { 2 } + 9 x } = \frac { } { x ( x + 9 ) ( x + 4 ) }$

Simplify. - $\frac { \frac { 10 } { a } + 10 } { \frac { 10 } { a } - 10 }$

Solve the equation. - $\frac { 5 x } { 7 } - 3 = x$

Solve. -A punch recipe calls for mixing 2 parts of orange juice with 7 parts of lemon juice. Find how much orange juice should be mixed with 56 ounces of lemon juice.

Perform the indicated operation. Simplify if possible. - $\frac { 11 } { 2 x - 11 } - \frac { 17 } { 11 - 2 x }$

Perform the indicated operation. Simplify if possible. - $\frac { 5 a + 4 b } { 2 } - \frac { 5 a - 4 b } { 2 }$

Perform the indicated operation. Simplify if possible. - $\frac { x + 4 } { 9 } + \frac { 3 } { 9 }$

Solve the proportion. - $\frac { x + 5 } { x } = \frac { 2 } { 3 }$

Convert as indicated. -1152 square inches=_____ square feet

Find the domain of the rational function. - $g ( x ) = \frac { x ^ { 2 } - 25 } { x ^ { 2 } - 15 x + 54 }$

Perform the indicated operations. Simplify if possible. - $\frac { 3 x } { x + 1 } + \frac { 4 } { x - 1 } - \frac { 6 } { x ^ { 2 } - 1 }$

Solve. -One number plus eighteen times its reciprocal is equal to nine.

Find the quotient and simplify. - $\frac { 35 m ^ { 2 } - 57 m n + 18 n ^ { 2 } } { 35 m ^ { 2 } - 43 m n + 12 n ^ { 2 } } \div \frac { 35 m ^ { 2 } - 12 m n - 36 n ^ { 2 } } { 49 m ^ { 2 } + 98 m n + 48 n ^ { 2 } }$

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

Perform the indicated operation. Simplify if possible. - $\frac { x } { x ^ { 2 } - 16 } - \frac { 5 } { x ^ { 2 } + 5 x + 4 }$

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

Simplify. - 2x+3x24x2−9x\frac { \frac { 2 } { x } + \frac { 3 } { x ^ { 2 } } } { \frac { 4 } { x ^ { 2 } } - \frac { 9 } { x } }x24​−x9​x2​+x23​​

Perform the indicated operation. Simplify if possible. - 5mm−6−30m−6\frac { 5 m } { m - 6 } - \frac { 30 } { m - 6 }m−65m​−m−630​

Solve the proportion. - 98=2x7\frac { 9 } { 8 } = \frac { 2 x } { 7 }89​=72x​