Question 1

Solve the equation.
-$\frac { 8 } { y + 3 } - \frac { 4 } { y - 3 } = \frac { 4 } { y ^ { 2 } - 9 }$

Accepted Answer

A)  $- 10$ 
B)  $\sqrt { 37 }$ 
C)  40 
D)  10 
A)  $- 10$ 
B)  $\sqrt { 37 }$ 
C)  40 
D)  10

Question 2

Solve.
-Jim can run 5 miles per hour on level ground on a still day. One windy day, he runs 11 miles with the wind, and in the same amount of time runs 7 miles against the wind. What is the rate of the wind?

Accepted Answer

A)  $1 \frac { 1 } { 9 } \mathrm { mph }$ 
B)  $2 \mathrm { mph }$ 
C)  $5 \mathrm { mph }$ 
D)  $22 \frac { 1 } { 2 } \mathrm { mph }$ 
A)  $1 \frac { 1 } { 9 } \mathrm { mph }$ 
B)  $2 \mathrm { mph }$ 
C)  $5 \mathrm { mph }$ 
D)  $22 \frac { 1 } { 2 } \mathrm { mph }$

Question 3

Find the domain of the rational expression.
-$f ( x ) = \frac { 4 x } { - 7 - x }$

Accepted Answer

A)  $\{ x \mid x$ is a real number and $x \neq 0 \}$ 
B)  $\{ x \mid x$ is a real number and $x \neq - 7 \}$ 
C)  $\{ x \mid x$ is a real number and $x \neq 0 , x \neq 7 \}$ 
D)  $\{ x \mid x$ is a real number and $x \neq 7 \}$ 
A)  $\{ x \mid x$ is a real number and $x \neq 0 \}$ 
B)  $\{ x \mid x$ is a real number and $x \neq - 7 \}$ 
C)  $\{ x \mid x$ is a real number and $x \neq 0 , x \neq 7 \}$ 
D)  $\{ x \mid x$ is a real number and $x \neq 7 \}$

Question 4

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

Accepted Answer

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

Question 5

Convert as indicated.
-In a physics lab, Shelly recorded the speed of an object at 150 feet per second. Convert this speed to miles per hour. (Round to the nearest whole, if necessary.)

Accepted Answer

A)  $2 \mathrm { mi } / \mathrm { hr }$ 
B)  $\frac { 5 } { 176 } \mathrm { mi } / \mathrm { hr }$ 
C)  $540,000 \mathrm { mi } / \mathrm { hr }$ 
D)  $102 \mathrm { mi } / \mathrm { hr }$ 
A)  $2 \mathrm { mi } / \mathrm { hr }$ 
B)  $\frac { 5 } { 176 } \mathrm { mi } / \mathrm { hr }$ 
C)  $540,000 \mathrm { mi } / \mathrm { hr }$ 
D)  $102 \mathrm { mi } / \mathrm { hr }$

Question 6

Perform the indicated operation and simplify if possible.
-$\frac { x + 6 } { x ^ { 2 } - 5 x + 6 } + \frac { 2 x - 5 } { x ^ { 2 } - 2 x - 3 }$

Accepted Answer

A)  $3 x + 1$ 
B)  $\frac { 3 x ^ { 2 } - 2 x + 16 } { ( x - 3 ) ( x - 2 ) ( x + 1 ) }$ 
C)  $\frac { 3 x ^ { 2 } - 2 x + 16 } { ( x + 3 ) ( x + 2 ) ( x - 1 ) }$ 
D)  $\frac { 3 x + 1 } { 2 x ^ { 2 } - 7 x + 3 }$ 
A)  $3 x + 1$ 
B)  $\frac { 3 x ^ { 2 } - 2 x + 16 } { ( x - 3 ) ( x - 2 ) ( x + 1 ) }$ 
C)  $\frac { 3 x ^ { 2 } - 2 x + 16 } { ( x + 3 ) ( x + 2 ) ( x - 1 ) }$ 
D)  $\frac { 3 x + 1 } { 2 x ^ { 2 } - 7 x + 3 }$

Question 7

Perform the indicated operation. Simplify if possible.
-$\frac { 72 } { 9 x } + \frac { 49 } { 7 x }$

Accepted Answer

A)  $\frac { 15 } { x }$ 
B)  $\frac { 945 } { 63 x }$ 
C)  $\frac { 15 } { x ^ { 2 } }$ 
D)  $\frac { 15 } { 2 x }$ 
A)  $\frac { 15 } { x }$ 
B)  $\frac { 945 } { 63 x }$ 
C)  $\frac { 15 } { x ^ { 2 } }$ 
D)  $\frac { 15 } { 2 x }$

Solve the equation. - $\frac { 8 } { y + 3 } - \frac { 4 } { y - 3 } = \frac { 4 } { y ^ { 2 } - 9 }$

Solve. -Jim can run 5 miles per hour on level ground on a still day. One windy day, he runs 11 miles with the wind, and in the same amount of time runs 7 miles against the wind. What is the rate of the wind?

Find the domain of the rational expression. - $f ( x ) = \frac { 4 x } { - 7 - x }$

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

Convert as indicated. -In a physics lab, Shelly recorded the speed of an object at 150 feet per second. Convert this speed to miles per hour. (Round to the nearest whole, if necessary.)

Perform the indicated operation and simplify if possible. - $\frac { x + 6 } { x ^ { 2 } - 5 x + 6 } + \frac { 2 x - 5 } { x ^ { 2 } - 2 x - 3 }$

Perform the indicated operation. Simplify if possible. - $\frac { 72 } { 9 x } + \frac { 49 } { 7 x }$

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

Solve the equation. - 8y+3−4y−3=4y2−9\frac { 8 } { y + 3 } - \frac { 4 } { y - 3 } = \frac { 4 } { y ^ { 2 } - 9 }y+38​−y−34​=y2−94​