Question 1

Simplify the rational expression.
-$\frac { a y - 3 a + 4 y - 12 } { a y - 3 a + 7 y - 21 }$

Accepted Answer

A)  $\frac { 4 y - 12 } { 7 y - 21 }$ 
B)  $\frac { ( a + 4 ) ( y - 3 ) } { ( a + 7 ) ( y + 3 ) }$ 
C)  $\frac { ( a + 4 ) ( y + 3 ) } { ( a + 7 ) ( y - 3 ) }$ 
D)  $\frac { a + 4 } { a + 7 }$ 
A)  $\frac { 4 y - 12 } { 7 y - 21 }$ 
B)  $\frac { ( a + 4 ) ( y - 3 ) } { ( a + 7 ) ( y + 3 ) }$ 
C)  $\frac { ( a + 4 ) ( y + 3 ) } { ( a + 7 ) ( y - 3 ) }$ 
D)  $\frac { a + 4 } { a + 7 }$

Question 2

Find the product and simplify.
-$\frac { x ^ { 2 } + 8 x + 12 } { x ^ { 2 } + 11 x + 18 } \cdot \frac { x ^ { 2 } + 9 x } { x ^ { 2 } - 2 x - 48 }$

Accepted Answer

A)  $\frac { x } { x ^ { 2 } + 11 x + 18 }$ 
B)  $\frac { x ( x + 9 ) } { x - 8 }$ 
C)  $\frac { x } { x - 8 }$ 
D)  $\frac { 1 } { x - 8 }$ 
A)  $\frac { x } { x ^ { 2 } + 11 x + 18 }$ 
B)  $\frac { x ( x + 9 ) } { x - 8 }$ 
C)  $\frac { x } { x - 8 }$ 
D)  $\frac { 1 } { x - 8 }$

Question 3

Find the domain of the rational expression.
-$f ( x ) = \frac { 3 x - 4 } { 8 }$

Accepted Answer

A)  $\{ x \mid x$ is a real number $\}$ 
B)  $\{ x \mid x$ is a real number and $x \neq 0 \}$ 
C)  $\{ x \mid x$ is a real number and $x \neq 8 \}$ 
D)  $\left\{ x \mid x \right.$ is a real number and $\left. x \neq \frac { 4 } { 3 } \right\}$ 
A)  $\{ x \mid x$ is a real number $\}$ 
B)  $\{ x \mid x$ is a real number and $x \neq 0 \}$ 
C)  $\{ x \mid x$ is a real number and $x \neq 8 \}$ 
D)  $\left\{ x \mid x \right.$ is a real number and $\left. x \neq \frac { 4 } { 3 } \right\}$

Question 4

Fill in the blank with one of the words or phrases listed below. Not all choices will be used. $$\begin{array} { l l l l } 
\text { least common denominator } & \text { simplifying } & \text { reciprocals } & \text { numerator } \
\text { cross products } & \text { ratio } & \text { proportion } & \text { denominator } \
\text { rational expression } & \text { domain } & \text { complex fraction } & \
\frac { - a } { b } & \frac { a } { - b } & \frac { - a } { - b } &
\end{array}$$
-The process of writing a rational expression in lowest terms is called .

Accepted Answer

A)  reciprocals 
B)  rational expression 
C)  simplifying 
D)  least common denominator 
A)  reciprocals 
B)  rational expression 
C)  simplifying 
D)  least common denominator

Question 5

Solve the equation.
-$\frac { x } { 2 x + 2 } = \frac { - 2 x } { 4 x + 4 } + \frac { 2 x - 3 } { x + 1 }$

Accepted Answer

A)  $- 3$ 
B)  no solution 
C)  3 
D)  $\frac { 3 } { 2 }$ 
A)  $- 3$ 
B)  no solution 
C)  3 
D)  $\frac { 3 } { 2 }$

Question 6

Find the least common denominator (LCD).
-$\frac { 3 x + 17 } { 6 x - 19 } , \frac { 2 x } { 6 x + 19 }$

Accepted Answer

A)  $( 6 x - 19 ) ( 6 x + 19 )$ 
B)  $2 x ( 3 x + 17 )$ 
C)  $2 x ( 3 x + 17 ) ( 6 x - 19 ) ( 6 x + 19 )$ 
D)  $( 6 x - 19 )$ or $( 6 x + 19 )$ 
A)  $( 6 x - 19 ) ( 6 x + 19 )$ 
B)  $2 x ( 3 x + 17 )$ 
C)  $2 x ( 3 x + 17 ) ( 6 x - 19 ) ( 6 x + 19 )$ 
D)  $( 6 x - 19 )$ or $( 6 x + 19 )$

Question 7

Solve.
-The ratio of the weight of an object on Earth to an object on Planet $X$ is 3 to 11 . If a person weighs 150 pounds on Earth, find his weight on Planet X. (Round to the nearest whole number, if necessary.)

Accepted Answer

A)  $5 \mathrm { lb }$ 
B)  $550 \mathrm { lb }$ 
C)  $4950 \mathrm { lb }$ 
D)  $41 \mathrm { lb }$ 
A)  $5 \mathrm { lb }$ 
B)  $550 \mathrm { lb }$ 
C)  $4950 \mathrm { lb }$ 
D)  $41 \mathrm { lb }$

Question 8

Solve.
-A bag of fertilizer covers 2000 square feet of lawn. Find how many bags of fertilizer should be purchased to cover a rectangular lawn 210 feet by 90 feet.

Accepted Answer

A)  95 bags 
B)  9 bags 
C)  10 bags 
D)  945 bags 
A)  95 bags 
B)  9 bags 
C)  10 bags 
D)  945 bags

Question 9

Find the product and simplify.
-$11 x ^ { 4 } \cdot \frac { x ^ { 2 } y } { 66 x ^ { 3 } y ^ { 2 } }$

Accepted Answer

A)  $\frac { x ^ { 3 } } { 6 y }$ 
B)  $\frac { 1 } { 66 x y }$ 
C)  $\frac { x ^ { 5 } } { 6 y }$ 
D)  $\frac { x ^ { 6 } y } { 6 x ^ { 3 } y ^ { 2 } }$ 
A)  $\frac { x ^ { 3 } } { 6 y }$ 
B)  $\frac { 1 } { 66 x y }$ 
C)  $\frac { x ^ { 5 } } { 6 y }$ 
D)  $\frac { x ^ { 6 } y } { 6 x ^ { 3 } y ^ { 2 } }$

Question 10

Convert as indicated.
-The meeting hall in the student union has 7200 square feet of floor space. Convert this to square yards.

Accepted Answer

A)  $21,600 \mathrm { sq } y d$ 
B)  $800 \mathrm { sq } \mathrm { yd }$ 
C)  64,800 sq yd 
D)  $2400 \mathrm { sq } \mathrm { yd }$ 
A)  $21,600 \mathrm { sq } y d$ 
B)  $800 \mathrm { sq } \mathrm { yd }$ 
C)  64,800 sq yd 
D)  $2400 \mathrm { sq } \mathrm { yd }$

Question 11

Simplify.
-$\frac { 1 - \frac { 5 } { x } } { x - \frac { 25 } { x } }$

Accepted Answer

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

Question 12

Simplify the complex fraction.
-$\frac { \frac { 3 } { a } + 3 } { \frac { 3 } { a } - 3 }$

Accepted Answer

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

Question 13

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

Accepted Answer

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

Question 14

Solve.
-One conveyor belt can move 1000 boxes in 7 minutes. Another can move 1000 boxes in 6 minutes. If another conveyor belt is added and all three are used, the boxes are moved in 3 minutes. How long would it take the third conveyor belt alone to do the same job?

Accepted Answer

A)  $42 \mathrm {~min}$ 
B)  $\frac { 1 } { 42 } \mathrm {~min}$ 
C)  $1 \frac { 5 } { 9 } \mathrm {~min}$ 
D)  $\frac { 9 } { 14 } \mathrm {~min}$ 
A)  $42 \mathrm {~min}$ 
B)  $\frac { 1 } { 42 } \mathrm {~min}$ 
C)  $1 \frac { 5 } { 9 } \mathrm {~min}$ 
D)  $\frac { 9 } { 14 } \mathrm {~min}$

Question 15

Simplify.
-$\frac { \frac { 3 } { x } + 7 } { \frac { 9 } { x ^ { 2 } } - 49 }$

Accepted Answer

A)  $\frac { x } { 3 - 7 x }$ 
B)  $\frac { x } { 3 x - 7 }$ 
C)  $\frac { 1 } { 3 x - 7 }$ 
D)  $\frac { 1 } { 3 - 7 x }$ 
A)  $\frac { x } { 3 - 7 x }$ 
B)  $\frac { x } { 3 x - 7 }$ 
C)  $\frac { 1 } { 3 x - 7 }$ 
D)  $\frac { 1 } { 3 - 7 x }$

Question 16

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

Accepted Answer

A)  $x = 12$ 
B)  $x = 16$ 
C)  $x = 4$ 
D)  $x = 11$ 
A)  $x = 12$ 
B)  $x = 16$ 
C)  $x = 4$ 
D)  $x = 11$

Question 17

Simplify.
-$\frac { \frac { 16 \mathrm {~s} ^ { 2 } - 49 \mathrm { r } ^ { 2 } } { \mathrm { rs } } } { \frac { 4 } { \mathrm { r } } - \frac { 7 } { \mathrm {~s} } }$

Accepted Answer

A)  $4 r + 7 s$ 
B)  $7 r + 4 s$ 
C)  $\frac { r s } { 4 r + 7 s }$ 
D)  $\frac { 7 r + 4 s } { r s }$ 
A)  $4 r + 7 s$ 
B)  $7 r + 4 s$ 
C)  $\frac { r s } { 4 r + 7 s }$ 
D)  $\frac { 7 r + 4 s } { r s }$

Question 18

Find the quotient and simplify.
-$\frac { 2 x ^ { 2 } } { 4 } \div \frac { x ^ { 3 } } { 20 }$

Accepted Answer

A)  $\frac { 10 } { x }$ 
B)  $\frac { x } { 10 }$ 
C)  $\frac { 40 x ^ { 2 } } { 4 x ^ { 3 } }$ 
D)  $\frac { 10 x ^ { 2 } } { x ^ { 3 } }$ 
A)  $\frac { 10 } { x }$ 
B)  $\frac { x } { 10 }$ 
C)  $\frac { 40 x ^ { 2 } } { 4 x ^ { 3 } }$ 
D)  $\frac { 10 x ^ { 2 } } { x ^ { 3 } }$

Question 19

Fill in the blank with one of the words or phrases listed below. Not all choices will be used. $$\begin{array} { l l l l } 
\text { least common denominator } & \text { simplifying } & \text { reciprocals } & \text { numerator } \
\text { cross products } & \text { ratio } & \text { proportion } & \text { denominator } \
\text { rational expression } & \text { domain } & \text { complex fraction } & \
\frac { - a } { b } & \frac { a } { - b } & \frac { - a } { - b } &
\end{array}$$
-The expressions $\frac { 2 x } { 7 }$ and $\frac { 7 } { 2 x }$ are called_______

Accepted Answer

A)  least common denominator 
B)  complex fraction 
C)  reciprocals 
D)  proportion 
A)  least common denominator 
B)  complex fraction 
C)  reciprocals 
D)  proportion

Question 20

Simplify the rational expression.
-$\frac { q - p } { p ^ { 2 } - q ^ { 2 } }$

Accepted Answer

A)  $\frac { 1 } { p + q }$ 
B)  $\frac { 1 } { q - p }$ 
C)  $- \frac { 1 } { p + q }$ 
D)  $\frac { 1 } { p - q }$ 
A)  $\frac { 1 } { p + q }$ 
B)  $\frac { 1 } { q - p }$ 
C)  $- \frac { 1 } { p + q }$ 
D)  $\frac { 1 } { p - q }$

Simplify the rational expression. - $\frac { a y - 3 a + 4 y - 12 } { a y - 3 a + 7 y - 21 }$

Find the product and simplify. - $\frac { x ^ { 2 } + 8 x + 12 } { x ^ { 2 } + 11 x + 18 } \cdot \frac { x ^ { 2 } + 9 x } { x ^ { 2 } - 2 x - 48 }$

Find the domain of the rational expression. - $f ( x ) = \frac { 3 x - 4 } { 8 }$

Solve the equation. - $\frac { x } { 2 x + 2 } = \frac { - 2 x } { 4 x + 4 } + \frac { 2 x - 3 } { x + 1 }$

Find the least common denominator (LCD). - $\frac { 3 x + 17 } { 6 x - 19 } , \frac { 2 x } { 6 x + 19 }$

Solve. -The ratio of the weight of an object on Earth to an object on Planet $X$ is 3 to 11 . If a person weighs 150 pounds on Earth, find his weight on Planet X. (Round to the nearest whole number, if necessary.)

Solve. -A bag of fertilizer covers 2000 square feet of lawn. Find how many bags of fertilizer should be purchased to cover a rectangular lawn 210 feet by 90 feet.

Find the product and simplify. - $11 x ^ { 4 } \cdot \frac { x ^ { 2 } y } { 66 x ^ { 3 } y ^ { 2 } }$

Convert as indicated. -The meeting hall in the student union has 7200 square feet of floor space. Convert this to square yards.

Simplify. - $\frac { 1 - \frac { 5 } { x } } { x - \frac { 25 } { x } }$

Simplify the complex fraction. - $\frac { \frac { 3 } { a } + 3 } { \frac { 3 } { a } - 3 }$

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

Solve. -One conveyor belt can move 1000 boxes in 7 minutes. Another can move 1000 boxes in 6 minutes. If another conveyor belt is added and all three are used, the boxes are moved in 3 minutes. How long would it take the third conveyor belt alone to do the same job?

Simplify. - $\frac { \frac { 3 } { x } + 7 } { \frac { 9 } { x ^ { 2 } } - 49 }$

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

Simplify. - $\frac { \frac { 16 \mathrm {~s} ^ { 2 } - 49 \mathrm { r } ^ { 2 } } { \mathrm { rs } } } { \frac { 4 } { \mathrm { r } } - \frac { 7 } { \mathrm {~s} } }$

Find the quotient and simplify. - $\frac { 2 x ^ { 2 } } { 4 } \div \frac { x ^ { 3 } } { 20 }$

Simplify the rational expression. - $\frac { q - p } { p ^ { 2 } - q ^ { 2 } }$

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 the rational expression. - ay−3a+4y−12ay−3a+7y−21\frac { a y - 3 a + 4 y - 12 } { a y - 3 a + 7 y - 21 }ay−3a+7y−21ay−3a+4y−12​

Find the product and simplify. - x2+8x+12x2+11x+18⋅x2+9xx2−2x−48\frac { x ^ { 2 } + 8 x + 12 } { x ^ { 2 } + 11 x + 18 } \cdot \frac { x ^ { 2 } + 9 x } { x ^ { 2 } - 2 x - 48 }x2+11x+18x2+8x+12​⋅x2−2x−48x2+9x​

Find the domain of the rational expression. - f(x)=3x−48f ( x ) = \frac { 3 x - 4 } { 8 }f(x)=83x−4​

Solve the equation. - x2x+2=−2x4x+4+2x−3x+1\frac { x } { 2 x + 2 } = \frac { - 2 x } { 4 x + 4 } + \frac { 2 x - 3 } { x + 1 }2x+2x​=4x+4−2x​+x+12x−3​

Find the least common denominator (LCD). - 3x+176x−19,2x6x+19\frac { 3 x + 17 } { 6 x - 19 } , \frac { 2 x } { 6 x + 19 }6x−193x+17​,6x+192x​

Solve. -The ratio of the weight of an object on Earth to an object on Planet XXX is 3 to 11 . If a person weighs 150 pounds on Earth, find his weight on Planet X. (Round to the nearest whole number, if necessary.)