Question 1

Simplify.
-$\left( a ^ { - 1 } + b ^ { - 1 } \right) ^ { - 1 }$

Accepted Answer

A)  $\frac { a b } { a - b }$ 
B)  $\frac { a b } { a }$ 
C)  $\frac { a + b } { a b }$ 
D)  $\frac { a b } { a + b }$ 
A)  $\frac { a b } { a - b }$ 
B)  $\frac { a b } { a }$ 
C)  $\frac { a + b } { a b }$ 
D)  $\frac { a b } { a + b }$

Question 2

List four equivalent forms for the rational expression.
-$- \frac { x - 7 } { x + 10 }$

Accepted Answer

A)  $\frac { - ( x - 7 ) } { x - 10 } , \frac { - x + 7 } { x + 10 } , \frac { x - 7 } { - ( x - 10 ) } , \frac { x - 7 } { - x - 10 }$ 
B)  $\frac { - ( x + 7 ) } { x + 10 } , \frac { - x + 7 } { x + 10 } , \frac { x + 7 } { - ( x + 10 ) } , \frac { x - 7 } { - x - 10 }$ 
C)  $\frac { - ( x - 7 ) } { x + 10 } , \frac { - x + 7 } { x + 10 } , \frac { x - 7 } { - ( x + 10 ) } , \frac { x - 7 } { - x - 10 }$ 
D)  $\frac { - ( x - 7 ) } { x + 10 } , \frac { - x + 7 } { x - 10 } , \frac { x - 7 } { - ( x - 10 ) } , \frac { x - 7 } { - x - 10 }$ 
A)  $\frac { - ( x - 7 ) } { x - 10 } , \frac { - x + 7 } { x + 10 } , \frac { x - 7 } { - ( x - 10 ) } , \frac { x - 7 } { - x - 10 }$ 
B)  $\frac { - ( x + 7 ) } { x + 10 } , \frac { - x + 7 } { x + 10 } , \frac { x + 7 } { - ( x + 10 ) } , \frac { x - 7 } { - x - 10 }$ 
C)  $\frac { - ( x - 7 ) } { x + 10 } , \frac { - x + 7 } { x + 10 } , \frac { x - 7 } { - ( x + 10 ) } , \frac { x - 7 } { - x - 10 }$ 
D)  $\frac { - ( x - 7 ) } { x + 10 } , \frac { - x + 7 } { x - 10 } , \frac { x - 7 } { - ( x - 10 ) } , \frac { x - 7 } { - x - 10 }$

Question 3

Convert as indicated.
-7 square feet =_____square inches

Accepted Answer

A)  1008 
B)  $\frac { 7 } { 144 }$ 
C)  49 
D)  84 
A)  1008 
B)  $\frac { 7 } { 144 }$ 
C)  49 
D)  84

Question 4

Solve the equation for the indicated variable.
-$\frac { \mathrm { P } _ { 1 } \mathrm {~V} _ { 1 } } { \mathrm {~T} _ { 1 } } = \frac { \mathrm { P } _ { 2 } \mathrm {~V} _ { 2 } } { \mathrm {~T} _ { 2 } } \quad$ for $\mathrm { V } _ { 2 }$

Accepted Answer

A)  $V _ { 2 } = \frac { P _ { 2 } V _ { 1 } T _ { 2 } } { P _ { 1 } T _ { 1 } }$ 
B)  $V _ { 2 } = \frac { P _ { 1 } V _ { 1 } T _ { 1 } } { P _ { 2 } T _ { 2 } }$ 
C)  $\mathrm { V } _ { 2 } = \frac { \mathrm { P } _ { 1 } \mathrm { P } _ { 2 } \mathrm {~T} _ { 2 } } { \mathrm {~V} _ { 1 } \mathrm {~T} _ { 1 } }$ 
D)  $V _ { 2 } = \frac { P _ { 1 } V _ { 1 } T _ { 2 } } { P _ { 2 } T _ { 1 } }$ 
A)  $V _ { 2 } = \frac { P _ { 2 } V _ { 1 } T _ { 2 } } { P _ { 1 } T _ { 1 } }$ 
B)  $V _ { 2 } = \frac { P _ { 1 } V _ { 1 } T _ { 1 } } { P _ { 2 } T _ { 2 } }$ 
C)  $\mathrm { V } _ { 2 } = \frac { \mathrm { P } _ { 1 } \mathrm { P } _ { 2 } \mathrm {~T} _ { 2 } } { \mathrm {~V} _ { 1 } \mathrm {~T} _ { 1 } }$ 
D)  $V _ { 2 } = \frac { P _ { 1 } V _ { 1 } T _ { 2 } } { P _ { 2 } T _ { 1 } }$

Question 5

Solve.
-Three out of 10 adults in a certain city buy their drugs at large drug stores. If this city has 138,000 adults, how many of these adults would you expect to buy their drugs at large drug stores?

Accepted Answer

A)  46,000 adults 
B)  41,400 adults 
C)  4600 adults 
D)  4140 adults 
A)  46,000 adults 
B)  41,400 adults 
C)  4600 adults 
D)  4140 adults

Question 6

Solve.
-The ratio of a quarterback's completed passes to attempted passes is 2 to 3 . If he attempted 6 passes, find how many passes he completed. Round to the nearest whole number if necessary.

Accepted Answer

A)  4 passes 
B)  3 passes 
C)  2 passes 
D)  9 passes 
A)  4 passes 
B)  3 passes 
C)  2 passes 
D)  9 passes

Question 7

Perform the indicated operation. Simplify if possible.
-$\frac { 3 x } { 7 } \cdot \frac { 5 x } { 7 }$

Accepted Answer

A)  $\frac { 15 x } { 49 }$ 
B)  $\frac { 15 x ^ { 2 } } { 7 }$ 
C)  $\frac { 15 x ^ { 2 } } { 49 }$ 
D)  $\frac { 8 x } { 7 }$ 
A)  $\frac { 15 x } { 49 }$ 
B)  $\frac { 15 x ^ { 2 } } { 7 }$ 
C)  $\frac { 15 x ^ { 2 } } { 49 }$ 
D)  $\frac { 8 x } { 7 }$

Question 8

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

Accepted Answer

A)  X=4 
B)  X=12 
C)  X=11 
D)  X=16 
A)  X=4 
B)  X=12 
C)  X=11 
D)  X=16

Question 9

Find the quotient and simplify.
-$( x + 1 ) \div \frac { x ^ { 2 } - 6 x + 5 } { 5 - x }$

Accepted Answer

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

Question 10

Perform the indicated operation. Simplify if possible.
-$\frac { 3 } { x + 6 } + 9$

Accepted Answer

A)  $\frac { 9 x + 51 } { x + 6 }$ 
B)  $\frac { 9 x + 72 } { x + 6 }$ 
C)  $\frac { 12 } { x + 6 }$ 
D)  $\frac { 9 x + 57 } { x + 6 }$ 
A)  $\frac { 9 x + 51 } { x + 6 }$ 
B)  $\frac { 9 x + 72 } { x + 6 }$ 
C)  $\frac { 12 } { x + 6 }$ 
D)  $\frac { 9 x + 57 } { x + 6 }$

Question 11

Convert as indicated.
-The field behind one of the dormitories at State College contains approximately 800 square yards of grass. Convert this to square feet.

Accepted Answer

A)  $7200 \mathrm { sq } \mathrm { ft }$ 
B)  $2400 \mathrm { sq } \mathrm { ft }$ 
C)  $266 \frac { 2 } { 3 } \mathrm { sq } \mathrm { ft }$ 
D)  $88 \frac { 8 } { 9 } \mathrm { sq } \mathrm { ft }$ 
A)  $7200 \mathrm { sq } \mathrm { ft }$ 
B)  $2400 \mathrm { sq } \mathrm { ft }$ 
C)  $266 \frac { 2 } { 3 } \mathrm { sq } \mathrm { ft }$ 
D)  $88 \frac { 8 } { 9 } \mathrm { sq } \mathrm { ft }$

Question 12

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

Accepted Answer

A)  $- 8$ 
B)  $- 6$ 
C)  6 
D)  8 
A)  $- 8$ 
B)  $- 6$ 
C)  6 
D)  8

Question 13

Find the quotient and simplify.
-$\frac { x ^ { 2 } - 10 x + 25 } { 11 x - 55 } \div \frac { 6 x - 30 } { 66 }$

Accepted Answer

A)  $\frac { x ^ { 2 } - 10 x + 25 } { ( x - 5 ) ^ { 2 } }$ 
B)  66 
C)  1 
D)  $\frac { ( x - 5 ) ^ { 2 } } { 121 }$ 
A)  $\frac { x ^ { 2 } - 10 x + 25 } { ( x - 5 ) ^ { 2 } }$ 
B)  66 
C)  1 
D)  $\frac { ( x - 5 ) ^ { 2 } } { 121 }$

Question 14

Rewrite the rational expression as an equivalent rational expression with the given denominator.
-$\frac { 9 } { 4 m } = \frac { } { 28 m }$

Accepted Answer

A)  $\frac { 63 } { 28 m }$ 
B)  $\frac { 4 } { 28 m }$ 
C)  $\frac { 7 } { 28 m }$ 
D)  $\frac { 9 } { 28 m }$ 
A)  $\frac { 63 } { 28 m }$ 
B)  $\frac { 4 } { 28 m }$ 
C)  $\frac { 7 } { 28 m }$ 
D)  $\frac { 9 } { 28 m }$

Question 15

Find the quotient and simplify.
-$\frac { p ^ { 2 } - 12 p + p q - 12 q } { 8 p ^ { 2 } - 8 q ^ { 2 } } \div \frac { p - 12 } { 11 p - 11 q }$

Accepted Answer

A)  $\frac { 11 } { 8 }$ 
B)  1 
C)  $\frac { 11 \left( p ^ { 2 } - 12 p + p q - 12 q \right) } { 8 ( p + q ) ( p - 12 ) }$ 
D)  $\frac { ( p - 12 ) ^ { 2 } } { 88 ( p - q ) ^ { 2 } }$ 
A)  $\frac { 11 } { 8 }$ 
B)  1 
C)  $\frac { 11 \left( p ^ { 2 } - 12 p + p q - 12 q \right) } { 8 ( p + q ) ( p - 12 ) }$ 
D)  $\frac { ( p - 12 ) ^ { 2 } } { 88 ( p - q ) ^ { 2 } }$

Question 16

Solve.
-To estimate the number of people in Springfield, population 10,000 , who have a swimming pool in their backyard, 250 people were interviewed. Of those polled, 125 had a swimming pool. How many people in the city might one expect to have a swimming pool? (Round to the nearest whole number, if necessary.)

Accepted Answer

A)  20,000 people 
B)  5000 people 
C)  500 people 
D)  3 people 
A)  20,000 people 
B)  5000 people 
C)  500 people 
D)  3 people

Question 17

Solve.
-One pump can drain a pool in 9 minutes. When a second pump is also used, the pool only takes 6 minutes to drain. How long would it take the second pump to drain the pool if it were the only pump in use?

Accepted Answer

A)  $3 \frac { 3 } { 5 } \mathrm {~min}$ 
B)  $\frac { 1 } { 18 } \mathrm {~min}$ 
C)  $51 \mathrm {~min}$ 
D)  $18 \mathrm {~min}$ 
A)  $3 \frac { 3 } { 5 } \mathrm {~min}$ 
B)  $\frac { 1 } { 18 } \mathrm {~min}$ 
C)  $51 \mathrm {~min}$ 
D)  $18 \mathrm {~min}$

Question 18

Find the domain of the rational expression.
-$f ( x ) = \frac { 5 x } { - 3 + x }$

Accepted Answer

A)  $\{ x \mid x$ is a real number and $x \neq - 3 \}$ 
B)  $\{ x \mid x$ is a real number and $x \neq 0 \}$ 
C)  $\{ x \mid x$ is a real number and $x \neq 3 \}$ 
D)  $\{ x \mid x$ is a real number and $x \neq 0 , x \neq 3 \}$ 
A)  $\{ x \mid x$ is a real number and $x \neq - 3 \}$ 
B)  $\{ x \mid x$ is a real number and $x \neq 0 \}$ 
C)  $\{ x \mid x$ is a real number and $x \neq 3 \}$ 
D)  $\{ x \mid x$ is a real number and $x \neq 0 , x \neq 3 \}$

Question 19

Find the quotient and simplify.
-$\frac { 40 x ^ { 4 } } { x ^ { 2 } - 1 } \div \frac { x ^ { 10 } } { ( x + 1 ) ^ { 2 } }$

Accepted Answer

A)  $\frac { 40 x ^ { 6 } ( x + 1 ) } { ( x - 1 ) }$ 
B)  $\frac { 40 x ^ { 40 } } { ( x - 1 ) ( x + 1 ) ^ { 3 } }$ 
C)  $\frac { 40 ( x + 1 ) } { x ^ { 6 } ( x - 1 ) }$ 
D)  $\frac { 4 ( x + 1 ) } { x ^ { 6 } ( x - 1 ) }$ 
A)  $\frac { 40 x ^ { 6 } ( x + 1 ) } { ( x - 1 ) }$ 
B)  $\frac { 40 x ^ { 40 } } { ( x - 1 ) ( x + 1 ) ^ { 3 } }$ 
C)  $\frac { 40 ( x + 1 ) } { x ^ { 6 } ( x - 1 ) }$ 
D)  $\frac { 4 ( x + 1 ) } { x ^ { 6 } ( x - 1 ) }$

Question 20

Simplify.
-$\frac { 3 x ^ { - 1 } + ( 8 y ) ^ { - 1 } } { x ^ { - 2 } }$

Accepted Answer

A)  $\frac { 3 x y + 8 x ^ { 2 } } { y }$ 
B)  $\frac { 8 y } { 24 x y + x ^ { 2 } }$ 
C)  $\frac { x ^ { 2 } } { 3 x + 8 y }$ 
D)  $\frac { 24 x y + x ^ { 2 } } { 8 y }$ 
A)  $\frac { 3 x y + 8 x ^ { 2 } } { y }$ 
B)  $\frac { 8 y } { 24 x y + x ^ { 2 } }$ 
C)  $\frac { x ^ { 2 } } { 3 x + 8 y }$ 
D)  $\frac { 24 x y + x ^ { 2 } } { 8 y }$

Simplify. - $\left( a ^ { - 1 } + b ^ { - 1 } \right) ^ { - 1 }$

List four equivalent forms for the rational expression. - $- \frac { x - 7 } { x + 10 }$

Convert as indicated. -7 square feet =_____square inches

Solve the equation for the indicated variable. - $\frac { \mathrm { P } _ { 1 } \mathrm {~V} _ { 1 } } { \mathrm {~T} _ { 1 } } = \frac { \mathrm { P } _ { 2 } \mathrm {~V} _ { 2 } } { \mathrm {~T} _ { 2 } } \quad$ for $\mathrm { V } _ { 2 }$

Solve. -Three out of 10 adults in a certain city buy their drugs at large drug stores. If this city has 138,000 adults, how many of these adults would you expect to buy their drugs at large drug stores?

Solve. -The ratio of a quarterback's completed passes to attempted passes is 2 to 3 . If he attempted 6 passes, find how many passes he completed. Round to the nearest whole number if necessary.

Perform the indicated operation. Simplify if possible. - $\frac { 3 x } { 7 } \cdot \frac { 5 x } { 7 }$

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

Find the quotient and simplify. - $( x + 1 ) \div \frac { x ^ { 2 } - 6 x + 5 } { 5 - x }$

Perform the indicated operation. Simplify if possible. - $\frac { 3 } { x + 6 } + 9$

Convert as indicated. -The field behind one of the dormitories at State College contains approximately 800 square yards of grass. Convert this to square feet.

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

Find the quotient and simplify. - $\frac { x ^ { 2 } - 10 x + 25 } { 11 x - 55 } \div \frac { 6 x - 30 } { 66 }$

Rewrite the rational expression as an equivalent rational expression with the given denominator. - $\frac { 9 } { 4 m } = \frac { } { 28 m }$

Find the quotient and simplify. - $\frac { p ^ { 2 } - 12 p + p q - 12 q } { 8 p ^ { 2 } - 8 q ^ { 2 } } \div \frac { p - 12 } { 11 p - 11 q }$

Solve. -One pump can drain a pool in 9 minutes. When a second pump is also used, the pool only takes 6 minutes to drain. How long would it take the second pump to drain the pool if it were the only pump in use?

Find the domain of the rational expression. - $f ( x ) = \frac { 5 x } { - 3 + x }$

Find the quotient and simplify. - $\frac { 40 x ^ { 4 } } { x ^ { 2 } - 1 } \div \frac { x ^ { 10 } } { ( x + 1 ) ^ { 2 } }$

Simplify. - $\frac { 3 x ^ { - 1 } + ( 8 y ) ^ { - 1 } } { x ^ { - 2 } }$

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. - (a−1+b−1)−1\left( a ^ { - 1 } + b ^ { - 1 } \right) ^ { - 1 }(a−1+b−1)−1

List four equivalent forms for the rational expression. - −x−7x+10- \frac { x - 7 } { x + 10 }−x+10x−7​