Question 1

Multiply: $$\frac { x ^ { 2 } - 6 x + 8 } { x ^ { 2 } - 7 x + 12 } \cdot \frac { x ^ { 2 } - 5 x + 6 } { x ^ { 2 } - 9 x + 14 }$$

Accepted Answer

A)  $\frac { x + 7 } { x - 2 }$ 
B)  $\frac { x - 3 } { x - 4 }$ 
C)  $\frac { x + 2 } { x + 7 }$ 
D)  $\frac { x - 2 } { x - 7 }$ 
E)  $\frac { x - 2 } { x - 4 }$ 
A)  $\frac { x + 7 } { x - 2 }$ 
B)  $\frac { x - 3 } { x - 4 }$ 
C)  $\frac { x + 2 } { x + 7 }$ 
D)  $\frac { x - 2 } { x - 7 }$ 
E)  $\frac { x - 2 } { x - 4 }$ D

Question 2

Indicate whether the statement is true or false.
A fraction can have the same variables in the numerator and denominator and be unsimplifiable.

Accepted Answer

A) True 
 B)False  True

Question 3

What inputs are defined for the expression? $$\frac { x } { 9 x + 4 }$$

Accepted Answer

A)  $R , x \neq - \frac { 9 } { 4 }$ 
B)  $R , x \neq \frac { 4 } { 9 }$ 
C)  $R , x \neq - \frac { 4 } { 9 }$ 
D)  $R, x \neq \frac { 9 } { 4 }$ 
E)  $ R , x \neq 0$ 
A)  $R , x \neq - \frac { 9 } { 4 }$ 
B)  $R , x \neq \frac { 4 } { 9 }$ 
C)  $R , x \neq - \frac { 4 } { 9 }$ 
D)  $R, x \neq \frac { 9 } { 4 }$ 
E)  $ R , x \neq 0$ C

Question 4

Use the properties of fractions to simplify the expression. The word per means division and may be replaced by a fraction bar. Round your answer to two decimal places if necessary. $$\frac { 5,200 \text { feet } } { 1,350 \text { feet per second } }$$

Accepted Answer

A)  3.85 sec 
B)  4.35 feet 
C)  2.65 sec 
D)  2.65 feet/sec 
E)  0.26 feet 
A)  3.85 sec 
B)  4.35 feet 
C)  2.65 sec 
D)  2.65 feet/sec 
E)  0.26 feet

Question 5

Multiply: $$\frac { 4 - n ^ { 2 } } { n ^ { 2 } - 7 n + 12 } \cdot \frac { n ^ { 2 } + 2 n - 15 } { n ^ { 2 } + 7 n + 10 }$$

Accepted Answer

A)  $\frac { ( 2 - n ) ( n - 3 ) ^ { 2 } } { ( n - 4 ) ( n + 2 ) ^ { 2 } }$ 
B)  $\frac { 2 - n } { n - 4 }$ 
C)  $\frac { 2 - n } { 4 - n }$ 
D)  $\frac { 5 - n } { 4 - n }$ 
E)  $\frac { 4 - n } { 2 - n }$ 
A)  $\frac { ( 2 - n ) ( n - 3 ) ^ { 2 } } { ( n - 4 ) ( n + 2 ) ^ { 2 } }$ 
B)  $\frac { 2 - n } { n - 4 }$ 
C)  $\frac { 2 - n } { 4 - n }$ 
D)  $\frac { 5 - n } { 4 - n }$ 
E)  $\frac { 4 - n } { 2 - n }$

Question 6

Suppose you have 6 miles to travel on a sometimes congested freeway. How long would it take you to travel that distance at the speed of 10 miles per hour?

Accepted Answer

A)  100 minutes 
B)  40 minutes 
C)  36 minutes 
D)  30 minutes 
E)  24 minutes 
A)  100 minutes 
B)  40 minutes 
C)  36 minutes 
D)  30 minutes 
E)  24 minutes

Question 7

What inputs are defined for the expression? $$\frac { 9 x } { x ^ { 2 } - 9 x + 18 }$$

Accepted Answer

A)  $R , x \neq 3 , x \neq 5$ 
B)  $R , x \neq 2 , x \neq 9$ 
C)  $R , x \neq 5 , x \neq 7$ 
D)  $R , x \neq - 2 , x \neq - 9$ 
E)  $R , x \neq 3 , x \neq 6$ 
A)  $R , x \neq 3 , x \neq 5$ 
B)  $R , x \neq 2 , x \neq 9$ 
C)  $R , x \neq 5 , x \neq 7$ 
D)  $R , x \neq - 2 , x \neq - 9$ 
E)  $R , x \neq 3 , x \neq 6$

Question 8

Use properties of fractions to simplify the expressions. The word per means division and may be replaced by a fraction bar. Round your answer to two decimal places. $$\frac { 25 \text { miles per hour } } { 10 \text { miles per gallon } }$$

Accepted Answer

A)  2.5 gal/hr 
B)  2.5 hr/gal 
C)  2 hr/gal 
D)  5 gal 
E)  3.5 gal/hr 
A)  2.5 gal/hr 
B)  2.5 hr/gal 
C)  2 hr/gal 
D)  5 gal 
E)  3.5 gal/hr

Question 9

Simplify. $$\frac { 2,000 \text { foot-pounds } } { 400 \text { pounds } }$$

Accepted Answer

A)  5 ft 
B)  500 foot-pounds 
C)  1600 foot-pounds 
D)  2 ft 
E)  5 foot-pounds 
A)  5 ft 
B)  500 foot-pounds 
C)  1600 foot-pounds 
D)  2 ft 
E)  5 foot-pounds

Question 10

What inputs are defined for the expression? $$\frac { x } { 3 x - 7 }$$

Accepted Answer

A)  $ R , x \neq - \frac { 7 } { 3 }$ 
B)  $  \mathrm { R } , x \neq - \frac { 3 } { 7 }$ 
C)  $R , x \neq \frac { 3 } { 7 }$ 
D)  $R , x \neq \frac { 7 } { 3 }$ 
E)  $ R , x \neq 0$ 
A)  $ R , x \neq - \frac { 7 } { 3 }$ 
B)  $  \mathrm { R } , x \neq - \frac { 3 } { 7 }$ 
C)  $R , x \neq \frac { 3 } { 7 }$ 
D)  $R , x \neq \frac { 7 } { 3 }$ 
E)  $ R , x \neq 0$

Question 11

Use properties of fractions to simplify the expressions. The word per means division and may be replaced by a fraction bar. Round your answer to two decimal places. $$\frac { 65 \text { words per minute } } { 400 \text { words per page } }$$

Accepted Answer

A)  0.16 page/min 
B)  0.16 min/page 
C)  0.21 min/page 
D)  6.15 min 
E)  0.21 page/min 
A)  0.16 page/min 
B)  0.16 min/page 
C)  0.21 min/page 
D)  6.15 min 
E)  0.21 page/min

Question 12

Simplify: $$\frac { 9 x } { x + 11 } - \frac { 11 x } { x + 11 }$$

Accepted Answer

A)  $- \frac { 99 x } { x + 11 }$ 
B)  $\frac { 2 x } { x + 11 }$ 
C)  $- \frac { 2 x } { x + 11 }$ 
D)  $0$ 
E)  $- \frac { 2 } { x + 11 }$ 
A)  $- \frac { 99 x } { x + 11 }$ 
B)  $\frac { 2 x } { x + 11 }$ 
C)  $- \frac { 2 x } { x + 11 }$ 
D)  $0$ 
E)  $- \frac { 2 } { x + 11 }$

Question 13

Simplify: $$\frac { 3 } { b } + \frac { 7 } { c }$$

Accepted Answer

A)  $\frac { 10 } { b + c }$ 
B)  $\frac { 10 } { b c }$ 
C)  $\frac { 3 c + 7 b } { b c }$ 
D)  $\frac { 3 b + 7 c } { b c }$ 
E)  $\frac { 3 c + 7 c } { b c }$ 
A)  $\frac { 10 } { b + c }$ 
B)  $\frac { 10 } { b c }$ 
C)  $\frac { 3 c + 7 b } { b c }$ 
D)  $\frac { 3 b + 7 c } { b c }$ 
E)  $\frac { 3 c + 7 c } { b c }$

Question 14

Divide: $$\frac { - 8 + 9 x - x ^ { 2 } } { x ^ { 2 } - 10 x + 16 } \div \frac { x ^ { 2 } - 4 x + 3 } { x ^ { 2 } - 3 x + 2 }$$

Accepted Answer

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

Question 15

Using a calculator to build a table and a graph or using a graphing calculator, describe the behavior of the graph of the equation as x approaches 5. $$y = - \frac { x } { x - 5 }$$

Accepted Answer

A)  Y approaches $+ \infty$ from the left and $- \infty$ from the right. 
B)  Y approaches $- \infty$ from the left and $+ \infty$ from the right. 
C)  Y approaches $- 5$ from the left and $5$ from the right. 
D)  Y approaches $5$ from the left and $- 5$ from the right. 
E)  Y approaches $- \infty$ from the left and $5$ from the right. 
A)  Y approaches $+ \infty$ from the left and $- \infty$ from the right. 
B)  Y approaches $- \infty$ from the left and $+ \infty$ from the right. 
C)  Y approaches $- 5$ from the left and $5$ from the right. 
D)  Y approaches $5$ from the left and $- 5$ from the right. 
E)  Y approaches $- \infty$ from the left and $5$ from the right.

Question 16

A potential landfill site contains 1,000,000 cubic yards of space. If a city with a population of 100,000 produces 400 cubic yards of garbage each day, how many years will the landfill last? Assume there are 365 days in a year. Please round your answer to nearest tenth.

Accepted Answer

A)  7.6 years 
B)  6.8 years 
C)  7.4 years 
D)  6.4 years 
E)  6.6 years 
A)  7.6 years 
B)  6.8 years 
C)  7.4 years 
D)  6.4 years 
E)  6.6 years

Question 17

Set up and solve an equation. Round to the nearest tenth. One farmer bales her hay in 15 days. A second farmer does it in 6 days. How many days will it take them working together?

Accepted Answer

A)  4.3 days 
B)  0.2 day 
C)  3.3 days 
D)  21 days 
E)  20 days 
A)  4.3 days 
B)  0.2 day 
C)  3.3 days 
D)  21 days 
E)  20 days

Question 18

Set up and solve an equation. Round to the nearest tenth. A $\frac { 5 } { 8 }$ -inch garden hose fills a child's pool in 1 hour. A $\frac { 1 } { 2 }$ -inch garden hose fills a child's pool in 1.2 hours. How long will it take to fill the pool if both hoses are used at once?

Accepted Answer

A)  0.4 hr 
B)  0.5 hr 
C)  1.8 hr 
D)  5.5 hr 
E)  4.5 hr 
A)  0.4 hr 
B)  0.5 hr 
C)  1.8 hr 
D)  5.5 hr 
E)  4.5 hr

Question 19

Simplify the expression. Assume the denominator is nonzero. $$\frac { ( x - 7 ) ( x + 1 ) } { ( x + 1 ) ( x + 7 ) }$$

Accepted Answer

A)  $\frac { x + 8 } { x + 5 }$ 
B)  $\frac { x - 7 } { x + 7 }$ 
C)  $\frac { x - 8 } { x + 7 }$ 
D)  $\frac { x - 7 } { x + 1 }$ 
E)  $\frac { x + 1 } { x + 7 }$ 
A)  $\frac { x + 8 } { x + 5 }$ 
B)  $\frac { x - 7 } { x + 7 }$ 
C)  $\frac { x - 8 } { x + 7 }$ 
D)  $\frac { x - 7 } { x + 1 }$ 
E)  $\frac { x + 1 } { x + 7 }$

Question 20

Indicate any inputs that must be excluded and then solve the equation. Factoring of the quadratic equation may be helpful. $$\frac { 9 - x } { x - 3 } = \frac { 6 } { x - 3 }$$

Accepted Answer

A)  $x \neq 0 , x = - 2 , x = 1$ 
B)  $x \neq 0 , x = - 1 , x = 1$ 
C)  $x \neq 3 , x = 1$ 
D)  $x \neq 3 ; x = 0$ 
E)  $x \neq 3 , \text { no solution }$ 
A)  $x \neq 0 , x = - 2 , x = 1$ 
B)  $x \neq 0 , x = - 1 , x = 1$ 
C)  $x \neq 3 , x = 1$ 
D)  $x \neq 3 ; x = 0$ 
E)  $x \neq 3 , \text { no solution }$

Multiply: $\frac { x ^ { 2 } - 6 x + 8 } { x ^ { 2 } - 7 x + 12 } \cdot \frac { x ^ { 2 } - 5 x + 6 } { x ^ { 2 } - 9 x + 14 }$

Indicate whether the statement is true or false. A fraction can have the same variables in the numerator and denominator and be unsimplifiable.

What inputs are defined for the expression? $\frac { x } { 9 x + 4 }$

Use the properties of fractions to simplify the expression. The word per means division and may be replaced by a fraction bar. Round your answer to two decimal places if necessary. $\frac { 5,200 \text { feet } } { 1,350 \text { feet per second } }$

Multiply: $\frac { 4 - n ^ { 2 } } { n ^ { 2 } - 7 n + 12 } \cdot \frac { n ^ { 2 } + 2 n - 15 } { n ^ { 2 } + 7 n + 10 }$

Suppose you have 6 miles to travel on a sometimes congested freeway. How long would it take you to travel that distance at the speed of 10 miles per hour?

What inputs are defined for the expression? $\frac { 9 x } { x ^ { 2 } - 9 x + 18 }$

Use properties of fractions to simplify the expressions. The word per means division and may be replaced by a fraction bar. Round your answer to two decimal places. $\frac { 25 \text { miles per hour } } { 10 \text { miles per gallon } }$

Simplify. $\frac { 2,000 \text { foot-pounds } } { 400 \text { pounds } }$

What inputs are defined for the expression? $\frac { x } { 3 x - 7 }$

Use properties of fractions to simplify the expressions. The word per means division and may be replaced by a fraction bar. Round your answer to two decimal places. $\frac { 65 \text { words per minute } } { 400 \text { words per page } }$

Simplify: $\frac { 9 x } { x + 11 } - \frac { 11 x } { x + 11 }$

Simplify: $\frac { 3 } { b } + \frac { 7 } { c }$

Divide: $\frac { - 8 + 9 x - x ^ { 2 } } { x ^ { 2 } - 10 x + 16 } \div \frac { x ^ { 2 } - 4 x + 3 } { x ^ { 2 } - 3 x + 2 }$

Using a calculator to build a table and a graph or using a graphing calculator, describe the behavior of the graph of the equation as x approaches 5. $y = - \frac { x } { x - 5 }$

A potential landfill site contains 1,000,000 cubic yards of space. If a city with a population of 100,000 produces 400 cubic yards of garbage each day, how many years will the landfill last? Assume there are 365 days in a year. Please round your answer to nearest tenth.

Set up and solve an equation. Round to the nearest tenth. One farmer bales her hay in 15 days. A second farmer does it in 6 days. How many days will it take them working together?

Set up and solve an equation. Round to the nearest tenth. A $\frac { 5 } { 8 }$ -inch garden hose fills a child's pool in 1 hour. A $\frac { 1 } { 2 }$ -inch garden hose fills a child's pool in 1.2 hours. How long will it take to fill the pool if both hoses are used at once?

Simplify the expression. Assume the denominator is nonzero. $\frac { ( x - 7 ) ( x + 1 ) } { ( x + 1 ) ( x + 7 ) }$

Indicate any inputs that must be excluded and then solve the equation. Factoring of the quadratic equation may be helpful. $\frac { 9 - x } { x - 3 } = \frac { 6 } { x - 3 }$

Algebraic Representations

Operations With Real Numbers

Solving Equations

Ratios, Rates, and Proportional Reasoning

Formulas, Functions, Linear Equations, and Inequalities in Two Variables

Systems of Equations

Polynomial Expressions

Squares and Square Roots

Filters

Exam 9: Rational Expressions

Multiply: x2−6x+8x2−7x+12⋅x2−5x+6x2−9x+14\frac { x ^ { 2 } - 6 x + 8 } { x ^ { 2 } - 7 x + 12 } \cdot \frac { x ^ { 2 } - 5 x + 6 } { x ^ { 2 } - 9 x + 14 }x2−7x+12x2−6x+8​⋅x2−9x+14x2−5x+6​

Indicate whether the statement is true or false. A fraction can have the same variables in the numerator and denominator and be unsimplifiable.

What inputs are defined for the expression? x9x+4\frac { x } { 9 x + 4 }9x+4x​

Multiply: 4−n2n2−7n+12⋅n2+2n−15n2+7n+10\frac { 4 - n ^ { 2 } } { n ^ { 2 } - 7 n + 12 } \cdot \frac { n ^ { 2 } + 2 n - 15 } { n ^ { 2 } + 7 n + 10 }n2−7n+124−n2​⋅n2+7n+10n2+2n−15​

Suppose you have 6 miles to travel on a sometimes congested freeway. How long would it take you to travel that distance at the speed of 10 miles per hour?

What inputs are defined for the expression? 9xx2−9x+18\frac { 9 x } { x ^ { 2 } - 9 x + 18 }x2−9x+189x​

Simplify. 2,000 foot-pounds 400 pounds \frac { 2,000 \text { foot-pounds } } { 400 \text { pounds } }400 pounds 2,000 foot-pounds ​

What inputs are defined for the expression? x3x−7\frac { x } { 3 x - 7 }3x−7x​

Simplify: 9xx+11−11xx+11\frac { 9 x } { x + 11 } - \frac { 11 x } { x + 11 }x+119x​−x+1111x​

Simplify: 3b+7c\frac { 3 } { b } + \frac { 7 } { c }b3​+c7​

Divide: −8+9x−x2x2−10x+16÷x2−4x+3x2−3x+2\frac { - 8 + 9 x - x ^ { 2 } } { x ^ { 2 } - 10 x + 16 } \div \frac { x ^ { 2 } - 4 x + 3 } { x ^ { 2 } - 3 x + 2 }x2−10x+16−8+9x−x2​÷x2−3x+2x2−4x+3​

Using a calculator to build a table and a graph or using a graphing calculator, describe the behavior of the graph of the equation as x approaches 5. y=−xx−5y = - \frac { x } { x - 5 }y=−x−5x​

A potential landfill site contains 1,000,000 cubic yards of space. If a city with a population of 100,000 produces 400 cubic yards of garbage each day, how many years will the landfill last? Assume there are 365 days in a year. Please round your answer to nearest tenth.

Set up and solve an equation. Round to the nearest tenth. One farmer bales her hay in 15 days. A second farmer does it in 6 days. How many days will it take them working together?

Set up and solve an equation. Round to the nearest tenth. A 58\frac { 5 } { 8 }85​ -inch garden hose fills a child's pool in 1 hour. A 12\frac { 1 } { 2 }21​ -inch garden hose fills a child's pool in 1.2 hours. How long will it take to fill the pool if both hoses are used at once?

Simplify the expression. Assume the denominator is nonzero. (x−7)(x+1)(x+1)(x+7)\frac { ( x - 7 ) ( x + 1 ) } { ( x + 1 ) ( x + 7 ) }(x+1)(x+7)(x−7)(x+1)​

Indicate any inputs that must be excluded and then solve the equation. Factoring of the quadratic equation may be helpful. 9−xx−3=6x−3\frac { 9 - x } { x - 3 } = \frac { 6 } { x - 3 }x−39−x​=x−36​

Algebraic Representations

Operations With Real Numbers

Solving Equations

Ratios, Rates, and Proportional Reasoning

Formulas, Functions, Linear Equations, and Inequalities in Two Variables

Systems of Equations

Polynomial Expressions

Squares and Square Roots

Filters

Multiply: $\frac { x ^ { 2 } - 6 x + 8 } { x ^ { 2 } - 7 x + 12 } \cdot \frac { x ^ { 2 } - 5 x + 6 } { x ^ { 2 } - 9 x + 14 }$

What inputs are defined for the expression? $\frac { x } { 9 x + 4 }$

Multiply: $\frac { 4 - n ^ { 2 } } { n ^ { 2 } - 7 n + 12 } \cdot \frac { n ^ { 2 } + 2 n - 15 } { n ^ { 2 } + 7 n + 10 }$

What inputs are defined for the expression? $\frac { 9 x } { x ^ { 2 } - 9 x + 18 }$

Simplify. $\frac { 2,000 \text { foot-pounds } } { 400 \text { pounds } }$

What inputs are defined for the expression? $\frac { x } { 3 x - 7 }$

Simplify: $\frac { 9 x } { x + 11 } - \frac { 11 x } { x + 11 }$

Simplify: $\frac { 3 } { b } + \frac { 7 } { c }$

Divide: $\frac { - 8 + 9 x - x ^ { 2 } } { x ^ { 2 } - 10 x + 16 } \div \frac { x ^ { 2 } - 4 x + 3 } { x ^ { 2 } - 3 x + 2 }$

Using a calculator to build a table and a graph or using a graphing calculator, describe the behavior of the graph of the equation as x approaches 5. $y = - \frac { x } { x - 5 }$

Set up and solve an equation. Round to the nearest tenth. A $\frac { 5 } { 8 }$ -inch garden hose fills a child's pool in 1 hour. A $\frac { 1 } { 2 }$ -inch garden hose fills a child's pool in 1.2 hours. How long will it take to fill the pool if both hoses are used at once?

Simplify the expression. Assume the denominator is nonzero. $\frac { ( x - 7 ) ( x + 1 ) } { ( x + 1 ) ( x + 7 ) }$

Indicate any inputs that must be excluded and then solve the equation. Factoring of the quadratic equation may be helpful. $\frac { 9 - x } { x - 3 } = \frac { 6 } { x - 3 }$