Question 1

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

Accepted Answer

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

Question 2

Solve.
-It is recommended that there be at least $9.3$ square feet of ground space in a garden for every newly planted shrub. A garden is $15.5$ feet by 18 feet. Find the maximum number of shrubs the garden can accommodate.

Accepted Answer

A)  11 shrubs 
B)  93 shrubs 
C)  30 shrubs 
D)  3 shrubs 
A)  11 shrubs 
B)  93 shrubs 
C)  30 shrubs 
D)  3 shrubs

Question 3

Find the least common denominator (LCD).
-$\frac { 8 } { x } , \frac { 9 } { x + 2 }$

Accepted Answer

A)  72 
B)  $x + 2$ 
C)  $x ( x + 2 )$ 
D)  $x$ 
A)  72 
B)  $x + 2$ 
C)  $x ( x + 2 )$ 
D)  $x$

Question 4

Find the domain of the rational expression.
-$f ( x ) = \frac { - 6 } { 5 x + 2 }$

Accepted Answer

A)  $\{ x \mid x$ is a real number and $x \neq 0 \}$ 
B) $\left\{ x \mid x \right.$ is a real number and $\left. x \neq - \frac { 2 } { 5 } \right\}$ 
C)  $\{ x \mid x$ is a real number and $x \neq 6 \}$ 
D)  $\left\{ x \mid x \right.$ is a real number and $\left. x \neq \frac { 2 } { 5 } \right\}$ 
A)  $\{ x \mid x$ is a real number and $x \neq 0 \}$ 
B) $\left\{ x \mid x \right.$ is a real number and $\left. x \neq - \frac { 2 } { 5 } \right\}$ 
C)  $\{ x \mid x$ is a real number and $x \neq 6 \}$ 
D)  $\left\{ x \mid x \right.$ is a real number and $\left. x \neq \frac { 2 } { 5 } \right\}$

Question 5

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

Accepted Answer

A)  $\left\{ x \mid x \right.$ is a real number and $\left. x z - \frac { 5 } { 3 } \right\}$ 
B)  $\left\{ x \mid x \right.$ is a real number and $\left. x \neq \frac { 3 } { 5 } , x \neq 0 \right\}$ 
C)  $\left\{ x \mid x \right.$ is a real number and $\left. x \neq \frac { 5 } { 3 } \right\}$ 
D)  $\left\{ x \mid x \right.$ is a real number and $\left. x \neq - \frac { 3 } { 5 } , x \neq 0 \right\}$ 
A)  $\left\{ x \mid x \right.$ is a real number and $\left. x z - \frac { 5 } { 3 } \right\}$ 
B)  $\left\{ x \mid x \right.$ is a real number and $\left. x \neq \frac { 3 } { 5 } , x \neq 0 \right\}$ 
C)  $\left\{ x \mid x \right.$ is a real number and $\left. x \neq \frac { 5 } { 3 } \right\}$ 
D)  $\left\{ x \mid x \right.$ is a real number and $\left. x \neq - \frac { 3 } { 5 } , x \neq 0 \right\}$

Question 6

Solve.
-The length of the rectangle is $\frac { 7 } { x - 4 }$ feet, while its width is $\frac { 5 } { x }$ feet. Find its perimeter.

Accepted Answer

A)  $\frac { 12 x - 20 } { x ( x - 4 ) } f t$ 
B)  $\frac { 24 x - 40 } { x ( x - 4 ) } f t$ 
C)  $\frac { 12 x - 20 } { x ( 4 - x ) } f t$ 
D)  $\frac { 24 x - 40 } { x ( 4 - x ) } f t$ 
A)  $\frac { 12 x - 20 } { x ( x - 4 ) } f t$ 
B)  $\frac { 24 x - 40 } { x ( x - 4 ) } f t$ 
C)  $\frac { 12 x - 20 } { x ( 4 - x ) } f t$ 
D)  $\frac { 24 x - 40 } { x ( 4 - x ) } f t$

Question 7

Solve the equation.
-$\frac { 7 } { y - 8 } = \frac { 5 } { y + 8 }$

Accepted Answer

A)  $- \frac { 4 } { 3 }$ 
B)  $- 48$ 
C)  48 
D)  $- 8$ 
A)  $- \frac { 4 } { 3 }$ 
B)  $- 48$ 
C)  48 
D)  $- 8$

Question 8

Perform the indicated operation. Simplify if possible.
-$\frac { 3 p } { 16 q } - \frac { 15 p } { 16 q }$

Accepted Answer

A)  $\frac { 9 p } { 8 q }$ 
B)  $- \frac { 3 p } { 4 q }$ 
C)  $\frac { 3 p } { 4 q }$ 
D)  $- \frac { 9 p } { 8 q }$ 
A)  $\frac { 9 p } { 8 q }$ 
B)  $- \frac { 3 p } { 4 q }$ 
C)  $\frac { 3 p } { 4 q }$ 
D)  $- \frac { 9 p } { 8 q }$

Question 9

Solve the proportion.
-$\frac { 1 } { x + 3 } = \frac { 3 } { 5 x }$

Accepted Answer

A)  $\frac { 3 } { 2 }$ 
B)  $\frac { 5 } { 4 }$ 
C)  $\frac { 9 } { 2 }$ 
D)  $\frac { 9 } { 8 }$ 
A)  $\frac { 3 } { 2 }$ 
B)  $\frac { 5 } { 4 }$ 
C)  $\frac { 9 } { 2 }$ 
D)  $\frac { 9 } { 8 }$

Question 10

Solve the problem.
-If $f ( x ) = \frac { x - 7 } { 7 x + 13 }$, find $f ( - 2 )$

Accepted Answer

A)  0 
B)  1 
C)  9 
D)  $- 9$ 
A)  0 
B)  1 
C)  9 
D)  $- 9$

Question 11

$$\text { Find and simplify the difference quotient } \frac { f ( a + h ) - f ( a ) } { h } , h \neq 0 \text { for the given function. }$$
-$f ( x ) = \frac { 2 } { x + 1 }$

Accepted Answer

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

Question 12

Find the domain of the rational expression.
-$f ( x ) = \frac { 1 - 2 x } { x ^ { 3 } - 2 x ^ { 2 } - 3 x }$

Accepted Answer

A)  $\{ x \mid x$ is a real number and $x \neq - 3 , x \neq - 1 , x \neq 0 \}$ 
B)  $\left\{ x \mid x \right.$ is a real number and $\left. x \neq 3 , x \neq - 1 , x \neq \frac { 1 } { 2 } , x \neq 0 \right\}$ 
C)  $\left\{ x \mid x \right.$ is a real number and $\left. x \neq 3 , x \neq - 1 , x \neq \frac { 1 } { 2 } \right\}$ 
D)  $\{ x \mid x$ is a real number and $x \neq 3 , x \neq - 1 , x \neq 0 \}$ 
A)  $\{ x \mid x$ is a real number and $x \neq - 3 , x \neq - 1 , x \neq 0 \}$ 
B)  $\left\{ x \mid x \right.$ is a real number and $\left. x \neq 3 , x \neq - 1 , x \neq \frac { 1 } { 2 } , x \neq 0 \right\}$ 
C)  $\left\{ x \mid x \right.$ is a real number and $\left. x \neq 3 , x \neq - 1 , x \neq \frac { 1 } { 2 } \right\}$ 
D)  $\{ x \mid x$ is a real number and $x \neq 3 , x \neq - 1 , x \neq 0 \}$

Question 13

Solve.
-Find the area of the rectangle.

Accepted Answer

A)  $\frac { 5 x ^ { 2 } } { 11 ( x - 7 ) } s q f t$ 
B)  $\frac { 5 } { 11 x ^ { 2 } ( x + 7 ) } s q f t$ 
C)  $\frac { 5 } { 11 x ^ { 2 } ( x - 7 ) } s q f t$ 
D)  $\frac { 7 } { 11 x ^ { 3 } - 77 } s q f t$ 
A)  $\frac { 5 x ^ { 2 } } { 11 ( x - 7 ) } s q f t$ 
B)  $\frac { 5 } { 11 x ^ { 2 } ( x + 7 ) } s q f t$ 
C)  $\frac { 5 } { 11 x ^ { 2 } ( x - 7 ) } s q f t$ 
D)  $\frac { 7 } { 11 x ^ { 3 } - 77 } s q f t$

Question 14

Solve.
-If three times a number added to 11 is divided by the number plus 9 , the result is four thirds. Find the number.

Accepted Answer

A)  $- \frac { 63 } { 5 }$ 
B)  $\frac { 3 } { 5 }$ 
C)  $- \frac { 17 } { 9 }$ 
D)  $- \frac { 33 } { 2 }$ 
A)  $- \frac { 63 } { 5 }$ 
B)  $\frac { 3 } { 5 }$ 
C)  $- \frac { 17 } { 9 }$ 
D)  $- \frac { 33 } { 2 }$

Question 15

Perform the indicated operation. Simplify if possible.
-$- \frac { 5 } { 6 } - \frac { 2 } { 3 x }$

Accepted Answer

A)  $\frac { - 5 x - 4 } { 6 x }$ 
B)  $\frac { - 5 x + 4 } { 6 x }$ 
C)  $\frac { 5 x - 4 } { 6 x }$ 
D)  $\frac { - 7 } { 6 - 3 x }$ 
A)  $\frac { - 5 x - 4 } { 6 x }$ 
B)  $\frac { - 5 x + 4 } { 6 x }$ 
C)  $\frac { 5 x - 4 } { 6 x }$ 
D)  $\frac { - 7 } { 6 - 3 x }$

Question 16

Solve.
-Five divided by the sum of a number and 4 , minus the quotient of 3 and the difference of the number and 4 is equal to 6 times the reciprocal of the difference of the number squared and 16 . What is the number?

Accepted Answer

A)  $- \frac { 13 } { 4 }$ 
B)  19 
C)  7 
D)  $- 13$ 
A)  $- \frac { 13 } { 4 }$ 
B)  19 
C)  7 
D)  $- 13$

Question 17

Simplify.
-$\frac { ( x + 2 ) ^ { - 1 } + ( x - 2 ) ^ { - 1 } } { \left( x ^ { 2 } - 4 \right) ^ { - 1 } }$

Accepted Answer

A)  4 
B)  $x ^ { 2 }$ 
C)  $2 x$ 
D)  $- 4$ 
A)  4 
B)  $x ^ { 2 }$ 
C)  $2 x$ 
D)  $- 4$

Question 18

Perform the indicated operation. Simplify if possible.
-$\frac { x ^ { 2 } - 11 x } { x - 5 } + \frac { 30 } { x - 5 }$

Accepted Answer

A)  $x - 5$ 
B)  $x + 5$ 
C)  $x - 6$ 
D)  $x + 6$ 
A)  $x - 5$ 
B)  $x + 5$ 
C)  $x - 6$ 
D)  $x + 6$

Question 19

Solve.
-A car travels 400 miles on level terrain in the same amount of time it travels 160 miles on mountainous terrain. If the rate of the car is 30 miles per hour less in the mountains than on level ground, find its rate in the mountains.

Accepted Answer

A)  $50 \mathrm { mph }$ 
B)  $80 \mathrm { mph }$ 
C)  $40 \mathrm { mph }$ 
D)  $20 \mathrm { mph }$ 
A)  $50 \mathrm { mph }$ 
B)  $80 \mathrm { mph }$ 
C)  $40 \mathrm { mph }$ 
D)  $20 \mathrm { mph }$

Question 20

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

Accepted Answer

A)  $\frac { 2 } { ( x + 5 ) ( x - 5 ) }$ 
B)  $\frac { 2 x - 30 } { ( x + 5 ) ( x - 5 ) }$ 
C)  $\frac { 2 x + 30 } { ( x + 5 ) ( x - 5 ) }$ 
D)  $\frac { 2 x - 10 } { ( x + 5 ) ( x - 5 ) }$ 
A)  $\frac { 2 } { ( x + 5 ) ( x - 5 ) }$ 
B)  $\frac { 2 x - 30 } { ( x + 5 ) ( x - 5 ) }$ 
C)  $\frac { 2 x + 30 } { ( x + 5 ) ( x - 5 ) }$ 
D)  $\frac { 2 x - 10 } { ( x + 5 ) ( x - 5 ) }$

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

Solve. -It is recommended that there be at least $9.3$ square feet of ground space in a garden for every newly planted shrub. A garden is $15.5$ feet by 18 feet. Find the maximum number of shrubs the garden can accommodate.

Find the least common denominator (LCD). - $\frac { 8 } { x } , \frac { 9 } { x + 2 }$

Find the domain of the rational expression. - $f ( x ) = \frac { - 6 } { 5 x + 2 }$

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

Solve. -The length of the rectangle is $\frac { 7 } { x - 4 }$ feet, while its width is $\frac { 5 } { x }$ feet. Find its perimeter. $Solve. -The length of the rectangle is \frac { 7 } { x - 4 } feet, while its width is \frac { 5 } { x } feet. Find its perimeter.$

Solve the equation. - $\frac { 7 } { y - 8 } = \frac { 5 } { y + 8 }$

Perform the indicated operation. Simplify if possible. - $\frac { 3 p } { 16 q } - \frac { 15 p } { 16 q }$

Solve the proportion. - $\frac { 1 } { x + 3 } = \frac { 3 } { 5 x }$

Solve the problem. -If $f ( x ) = \frac { x - 7 } { 7 x + 13 }$ , find $f ( - 2 )$

$\text { Find and simplify the difference quotient } \frac { f ( a + h ) - f ( a ) } { h } , h \neq 0 \text { for the given function. }$ - $f ( x ) = \frac { 2 } { x + 1 }$

Find the domain of the rational expression. - $f ( x ) = \frac { 1 - 2 x } { x ^ { 3 } - 2 x ^ { 2 } - 3 x }$

Solve. -Find the area of the rectangle.

Solve. -If three times a number added to 11 is divided by the number plus 9 , the result is four thirds. Find the number.

Perform the indicated operation. Simplify if possible. - $- \frac { 5 } { 6 } - \frac { 2 } { 3 x }$

Solve. -Five divided by the sum of a number and 4 , minus the quotient of 3 and the difference of the number and 4 is equal to 6 times the reciprocal of the difference of the number squared and 16 . What is the number?

Simplify. - $\frac { ( x + 2 ) ^ { - 1 } + ( x - 2 ) ^ { - 1 } } { \left( x ^ { 2 } - 4 \right) ^ { - 1 } }$

Perform the indicated operation. Simplify if possible. - $\frac { x ^ { 2 } - 11 x } { x - 5 } + \frac { 30 } { x - 5 }$

Solve. -A car travels 400 miles on level terrain in the same amount of time it travels 160 miles on mountainous terrain. If the rate of the car is 30 miles per hour less in the mountains than on level ground, find its rate in the mountains.

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

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

Perform the indicated operation. Simplify if possible. - 2x2−6x\frac { 2 } { x ^ { 2 } } - \frac { 6 } { x }x22​−x6​

Solve. -It is recommended that there be at least 9.39.39.3 square feet of ground space in a garden for every newly planted shrub. A garden is 15.515.515.5 feet by 18 feet. Find the maximum number of shrubs the garden can accommodate.

Find the least common denominator (LCD). - 8x,9x+2\frac { 8 } { x } , \frac { 9 } { x + 2 }x8​,x+29​

Find the domain of the rational expression. - f(x)=−65x+2f ( x ) = \frac { - 6 } { 5 x + 2 }f(x)=5x+2−6​

Find the domain of the rational expression. - f(x)=x3x−5f ( x ) = \frac { x } { 3 x - 5 }f(x)=3x−5x​

Solve. -The length of the rectangle is 7x−4\frac { 7 } { x - 4 }x−47​ feet, while its width is 5x\frac { 5 } { x }x5​ feet. Find its perimeter.

Solve the equation. - 7y−8=5y+8\frac { 7 } { y - 8 } = \frac { 5 } { y + 8 }y−87​=y+85​

Perform the indicated operation. Simplify if possible. - 3p16q−15p16q\frac { 3 p } { 16 q } - \frac { 15 p } { 16 q }16q3p​−16q15p​

Solve the proportion. - 1x+3=35x\frac { 1 } { x + 3 } = \frac { 3 } { 5 x }x+31​=5x3​

Solve the problem. -If f(x)=x−77x+13f ( x ) = \frac { x - 7 } { 7 x + 13 }f(x)=7x+13x−7​ , find f(−2)f ( - 2 )f(−2)

Find the domain of the rational expression. - f(x)=1−2xx3−2x2−3xf ( x ) = \frac { 1 - 2 x } { x ^ { 3 } - 2 x ^ { 2 } - 3 x }f(x)=x3−2x2−3x1−2x​