Question 1

Find the product and simplify.
-$\frac { 4 x + 6 y } { x ^ { 2 } + 6 x y + 9 y ^ { 2 } } \cdot \frac { x + 3 y } { 3 }$

Accepted Answer

A)  $\frac { 4 x ^ { 2 } + 18 x y + 18 y ^ { 2 } } { 3 x ^ { 2 } + 18 x y + 27 y ^ { 2 } }$ 
B)  $\frac { 6 } { 18 x y }$ 
C)  $\frac { 4 x + 6 y } { 3 ( x + 3 y ) }$ 
D)  $\frac { 4 x ^ { 2 } + 18 x y } { 3 x ^ { 2 } + 18 x y + 27 y ^ { 2 } }$ 
A)  $\frac { 4 x ^ { 2 } + 18 x y + 18 y ^ { 2 } } { 3 x ^ { 2 } + 18 x y + 27 y ^ { 2 } }$ 
B)  $\frac { 6 } { 18 x y }$ 
C)  $\frac { 4 x + 6 y } { 3 ( x + 3 y ) }$ 
D)  $\frac { 4 x ^ { 2 } + 18 x y } { 3 x ^ { 2 } + 18 x y + 27 y ^ { 2 } }$

Question 2

Simplify.
-$\frac { \frac { 2 } { x + 3 } + \frac { 4 } { x + 7 } } { \frac { 3 x + 13 } { x ^ { 2 } + 10 x + 21 } }$

Accepted Answer

A)  $\frac { 1 } { 2 }$ 
B)  2 
C)  $3 x + 13$ 
D)  6 
A)  $\frac { 1 } { 2 }$ 
B)  2 
C)  $3 x + 13$ 
D)  6

Question 3

Rewrite the rational expression as an equivalent rational expression with the given denominator.
-$\frac { 3 } { 3 x } = \frac { } { 15 x ^ { 2 } }$

Accepted Answer

A)  $\frac { 15 } { 15 x ^ { 2 } }$ 
B)  $\frac { 3 } { 15 x ^ { 2 } }$ 
C)  $\frac { 15 x } { 15 x ^ { 2 } }$ 
D)  $\frac { 3 x ^ { 2 } } { 15 x ^ { 2 } }$ 
A)  $\frac { 15 } { 15 x ^ { 2 } }$ 
B)  $\frac { 3 } { 15 x ^ { 2 } }$ 
C)  $\frac { 15 x } { 15 x ^ { 2 } }$ 
D)  $\frac { 3 x ^ { 2 } } { 15 x ^ { 2 } }$

Question 4

Find the quotient and simplify.
-$\frac { ( x + 9 ) ( x + 2 ) } { 3 x } \div \frac { 2 x + 18 } { 6 x ^ { 6 } }$

Accepted Answer

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

Question 5

Perform the indicated operation and simplify if possible.
-$\frac { 3 } { x - 2 } \cdot ( 4 x - 8 )$

Accepted Answer

A)  4 
B)  3 
C)  8 
D)  12 
A)  4 
B)  3 
C)  8 
D)  12

Question 6

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

Accepted Answer

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

Question 7

Perform the indicated operation. Simplify if possible.
-$\frac { 8 x } { x - 8 } - \frac { 64 } { x - 8 }$

Accepted Answer

A)  $\frac { 1 } { 8 }$ 
B)  $\frac { 8 x - 64 } { x - 16 }$ 
C)  $8 x$ 
D)  8 
A)  $\frac { 1 } { 8 }$ 
B)  $\frac { 8 x - 64 } { x - 16 }$ 
C)  $8 x$ 
D)  8

Question 8

Solve the problem.
-To calculate the drug dosage for a child, a pharmacist may use the formula $d ( x ) = \frac { D x } { x + 12 } , 0 \leq x \leq 12$.
The child's age is $x$ and the adult dosage is D. What is the dosage for an 4 -year old child if the adult dosage is $90 \mathrm { mg }$ ? (Round to the nearest tenth.)

Accepted Answer

A)  $5.6 \mathrm { mg }$ 
B)  $22.5 \mathrm { mg }$ 
C)  $30.0 \mathrm { mg }$ 
D)  $90.0 \mathrm { mg }$ 
A)  $5.6 \mathrm { mg }$ 
B)  $22.5 \mathrm { mg }$ 
C)  $30.0 \mathrm { mg }$ 
D)  $90.0 \mathrm { mg }$

Question 9

Solve the equation for the indicated variable.
-$V = \frac { B h } { 3 } \quad$ for $h$

Accepted Answer

A)  $h = \frac { 3 V } { B }$ 
B)  $h = \frac { B } { 3 V }$ 
C)  $h = \frac { V } { 3 B }$ 
D)  $h = \frac { 3 B } { V }$ 
A)  $h = \frac { 3 V } { B }$ 
B)  $h = \frac { B } { 3 V }$ 
C)  $h = \frac { V } { 3 B }$ 
D)  $h = \frac { 3 B } { V }$

Question 10

Perform the indicated operation. Simplify if possible.
-$\frac { 6 } { 49 x ^ { 2 } - 1 } + \frac { 8 } { 1 - 49 x ^ { 2 } }$

Accepted Answer

A)  $\frac { 14 } { 49 x ^ { 2 } - 1 }$ 
B)  $- \frac { 2 } { 49 x ^ { 2 } - 1 }$ 
C)  $- \frac { 14 } { 49 x ^ { 2 } - 1 }$ 
D)  $\frac { 2 } { 49 x ^ { 2 } - 1 }$ 
A)  $\frac { 14 } { 49 x ^ { 2 } - 1 }$ 
B)  $- \frac { 2 } { 49 x ^ { 2 } - 1 }$ 
C)  $- \frac { 14 } { 49 x ^ { 2 } - 1 }$ 
D)  $\frac { 2 } { 49 x ^ { 2 } - 1 }$

Question 11

Perform the indicated operation. Simplify if possible.
-$\frac { 3 x + 4 } { 2 } - \frac { 3 x - 4 } { 2 }$

Accepted Answer

A)  $3 x$ 
B)  0 
C)  4 
D)  16 
A)  $3 x$ 
B)  0 
C)  4 
D)  16

Question 12

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

Accepted Answer

A)  $\frac { 8 } { x - 3 }$ 
B)  0 
C)  $- \frac { 8 } { x - 3 }$ 
D)  $\frac { 4 } { x - 3 }$ 
A)  $\frac { 8 } { x - 3 }$ 
B)  0 
C)  $- \frac { 8 } { x - 3 }$ 
D)  $\frac { 4 } { x - 3 }$

Question 13

Find the domain of the rational expression.
-$f ( y ) = \frac { y ^ { 2 } - 24 y } { 4 y }$

Accepted Answer

A)  $\{ y \mid y$ is a real number and $y \neq 0 \}$ 
B)  $\{ \mathrm { y } \mid \mathrm { y }$ is a real number and $\mathrm { y } \neq 0$ and $\mathrm { y } \neq 24 \}$ 
C)  $\{ \mathrm { y } \mid \mathrm { y }$ is a real number and $\mathrm { y } \neq 4 \}$ 
D)  $\left\{ \mathrm { y } \mid \mathrm { y } \right.$ is a real number and $\left. \mathrm { y } \neq \frac { 1 } { 4 } \right\}$ 
A)  $\{ y \mid y$ is a real number and $y \neq 0 \}$ 
B)  $\{ \mathrm { y } \mid \mathrm { y }$ is a real number and $\mathrm { y } \neq 0$ and $\mathrm { y } \neq 24 \}$ 
C)  $\{ \mathrm { y } \mid \mathrm { y }$ is a real number and $\mathrm { y } \neq 4 \}$ 
D)  $\left\{ \mathrm { y } \mid \mathrm { y } \right.$ is a real number and $\left. \mathrm { y } \neq \frac { 1 } { 4 } \right\}$

Question 14

Simplify the expression.
-$\frac { y ^ { 3 } - 8 } { y - 2 }$

Accepted Answer

A)  $\frac { y ^ { 3 } - 8 } { y - 2 }$ 
B)  $y ^ { 2 } + 2 y + 4$ 
C)  $y ^ { 2 } - 4$ 
D)  $\frac { 1 } { y - 2 }$ 
A)  $\frac { y ^ { 3 } - 8 } { y - 2 }$ 
B)  $y ^ { 2 } + 2 y + 4$ 
C)  $y ^ { 2 } - 4$ 
D)  $\frac { 1 } { y - 2 }$

Question 15

Solve.
-A can of lemonade comes with a measuring scoop and directions for mixing are 4 scoops of mix for every 32 cups of water. How much water is needed to make the entire can of lemonade if there are 40 scoops of mix?

Accepted Answer

A)  160 cups 
B)  320 cups 
C)  5 cups 
D)  1280 cups 
A)  160 cups 
B)  320 cups 
C)  5 cups 
D)  1280 cups

Question 16

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

Accepted Answer

A)  0 
B)  2 
C)  $- 6$ 
D)  6 
A)  0 
B)  2 
C)  $- 6$ 
D)  6

Question 17

Simplify.
-$\frac { 4 + \frac { 2 } { x } } { \frac { x } { 4 } + \frac { 1 } { 8 } }$

Accepted Answer

A)  1 
B)  $\frac { 16 } { x }$ 
C)  $\frac { x } { 16 }$ 
D)  16 
A)  1 
B)  $\frac { 16 } { x }$ 
C)  $\frac { x } { 16 }$ 
D)  16

Question 18

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

Accepted Answer

A)  $\frac { 11 x - 10 } { ( x - 1 ) ( x + 1 ) ( x - 2 ) }$ 
B)  $\frac { 10 x - 11 } { ( x - 1 ) ( x + 1 ) ( x - 2 ) }$ 
C)  $\frac { 56 x - 10 } { ( x - 1 ) ( x + 1 ) ( x - 2 ) }$ 
D)  $\frac { 11 x - 10 } { ( x - 1 ) ( x - 2 ) }$ 
A)  $\frac { 11 x - 10 } { ( x - 1 ) ( x + 1 ) ( x - 2 ) }$ 
B)  $\frac { 10 x - 11 } { ( x - 1 ) ( x + 1 ) ( x - 2 ) }$ 
C)  $\frac { 56 x - 10 } { ( x - 1 ) ( x + 1 ) ( x - 2 ) }$ 
D)  $\frac { 11 x - 10 } { ( x - 1 ) ( x - 2 ) }$

Question 19

Simplify the expression.
-$\frac { ( y + 8 ) ( y - 2 ) } { ( y - 2 ) ( y + 3 ) }$

Accepted Answer

A)  $\frac { y + 2 } { y + 1 }$ 
B)  $\frac { 2 y - 2 } { 2 y + 1 }$ 
C)  $\frac { y - 8 } { y - 3 }$ 
D)  $\frac { y + 8 } { y + 3 }$ 
A)  $\frac { y + 2 } { y + 1 }$ 
B)  $\frac { 2 y - 2 } { 2 y + 1 }$ 
C)  $\frac { y - 8 } { y - 3 }$ 
D)  $\frac { y + 8 } { y + 3 }$

Question 20

Find the product and simplify.
-$\frac { 3 x ^ { 2 } } { 4 } \cdot \frac { 8 } { x ^ { 3 } }$

Accepted Answer

A)  $\frac { 6 x ^ { 2 } } { x ^ { 3 } }$ 
B)  $\frac { 6 } { x }$ 
C)  $\frac { x } { 6 }$ 
D)  $\frac { 24 x ^ { 2 } } { 4 x ^ { 3 } }$ 
A)  $\frac { 6 x ^ { 2 } } { x ^ { 3 } }$ 
B)  $\frac { 6 } { x }$ 
C)  $\frac { x } { 6 }$ 
D)  $\frac { 24 x ^ { 2 } } { 4 x ^ { 3 } }$

Find the product and simplify. - $\frac { 4 x + 6 y } { x ^ { 2 } + 6 x y + 9 y ^ { 2 } } \cdot \frac { x + 3 y } { 3 }$

Simplify. - $\frac { \frac { 2 } { x + 3 } + \frac { 4 } { x + 7 } } { \frac { 3 x + 13 } { x ^ { 2 } + 10 x + 21 } }$

Rewrite the rational expression as an equivalent rational expression with the given denominator. - $\frac { 3 } { 3 x } = \frac { } { 15 x ^ { 2 } }$

Find the quotient and simplify. - $\frac { ( x + 9 ) ( x + 2 ) } { 3 x } \div \frac { 2 x + 18 } { 6 x ^ { 6 } }$

Perform the indicated operation and simplify if possible. - $\frac { 3 } { x - 2 } \cdot ( 4 x - 8 )$

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

Perform the indicated operation. Simplify if possible. - $\frac { 8 x } { x - 8 } - \frac { 64 } { x - 8 }$

Solve the equation for the indicated variable. - $V = \frac { B h } { 3 } \quad$ for $h$

Perform the indicated operation. Simplify if possible. - $\frac { 6 } { 49 x ^ { 2 } - 1 } + \frac { 8 } { 1 - 49 x ^ { 2 } }$

Perform the indicated operation. Simplify if possible. - $\frac { 3 x + 4 } { 2 } - \frac { 3 x - 4 } { 2 }$

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

Find the domain of the rational expression. - $f ( y ) = \frac { y ^ { 2 } - 24 y } { 4 y }$

Simplify the expression. - $\frac { y ^ { 3 } - 8 } { y - 2 }$

Solve. -A can of lemonade comes with a measuring scoop and directions for mixing are 4 scoops of mix for every 32 cups of water. How much water is needed to make the entire can of lemonade if there are 40 scoops of mix?

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

Simplify. - $\frac { 4 + \frac { 2 } { x } } { \frac { x } { 4 } + \frac { 1 } { 8 } }$

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

Simplify the expression. - $\frac { ( y + 8 ) ( y - 2 ) } { ( y - 2 ) ( y + 3 ) }$

Find the product and simplify. - $\frac { 3 x ^ { 2 } } { 4 } \cdot \frac { 8 } { x ^ { 3 } }$

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 product and simplify. - 4x+6yx2+6xy+9y2⋅x+3y3\frac { 4 x + 6 y } { x ^ { 2 } + 6 x y + 9 y ^ { 2 } } \cdot \frac { x + 3 y } { 3 }x2+6xy+9y24x+6y​⋅3x+3y​

Simplify. - 2x+3+4x+73x+13x2+10x+21\frac { \frac { 2 } { x + 3 } + \frac { 4 } { x + 7 } } { \frac { 3 x + 13 } { x ^ { 2 } + 10 x + 21 } }x2+10x+213x+13​x+32​+x+74​​

Rewrite the rational expression as an equivalent rational expression with the given denominator. - 33x=15x2\frac { 3 } { 3 x } = \frac { } { 15 x ^ { 2 } }3x3​=15x2​

Find the quotient and simplify. - (x+9)(x+2)3x÷2x+186x6\frac { ( x + 9 ) ( x + 2 ) } { 3 x } \div \frac { 2 x + 18 } { 6 x ^ { 6 } }3x(x+9)(x+2)​÷6x62x+18​

Perform the indicated operation and simplify if possible. - 3x−2⋅(4x−8)\frac { 3 } { x - 2 } \cdot ( 4 x - 8 )x−23​⋅(4x−8)

Perform the indicated operation. Simplify if possible. - 7x−2\frac { 7 } { x } - 2x7​−2

Perform the indicated operation. Simplify if possible. - 8xx−8−64x−8\frac { 8 x } { x - 8 } - \frac { 64 } { x - 8 }x−88x​−x−864​

Solve the equation for the indicated variable. - V=Bh3V = \frac { B h } { 3 } \quadV=3Bh​ for hhh

Perform the indicated operation. Simplify if possible. - 649x2−1+81−49x2\frac { 6 } { 49 x ^ { 2 } - 1 } + \frac { 8 } { 1 - 49 x ^ { 2 } }49x2−16​+1−49x28​

Perform the indicated operation. Simplify if possible. - 3x+42−3x−42\frac { 3 x + 4 } { 2 } - \frac { 3 x - 4 } { 2 }23x+4​−23x−4​

Perform the indicated operation. Simplify if possible. - 4x−3+43−x\frac { 4 } { x - 3 } + \frac { 4 } { 3 - x }x−34​+3−x4​

Find the domain of the rational expression. - f(y)=y2−24y4yf ( y ) = \frac { y ^ { 2 } - 24 y } { 4 y }f(y)=4yy2−24y​

Simplify the expression. - y3−8y−2\frac { y ^ { 3 } - 8 } { y - 2 }y−2y3−8​