Question 1

Simplify the rational expression. $\frac { 18 x ^ { 3 } y ^ { 6 } } { 45 x ^ { 5 } y ^ { 9 } }$

Accepted Answer

A)  $\frac { 5 } { 2 } x ^ { 2 } y ^ { 3 } \quad ($ Provided $x \neq 0 , y \neq 0$ ) 
B)  $\frac { 2 } { 5 x ^ { 2 } y ^ { 3 } }$ 
C)  $\frac { 18 } { 45 x ^ { 2 } y ^ { 3 } }$ 
D)  $\frac { 2 x ^ { 2 } } { 5 y ^ { 3 } } \quad$ (Provided $\left. x \neq 0 \right)$ 
A)  $\frac { 5 } { 2 } x ^ { 2 } y ^ { 3 } \quad ($ Provided $x \neq 0 , y \neq 0$ ) 
B)  $\frac { 2 } { 5 x ^ { 2 } y ^ { 3 } }$ 
C)  $\frac { 18 } { 45 x ^ { 2 } y ^ { 3 } }$ 
D)  $\frac { 2 x ^ { 2 } } { 5 y ^ { 3 } } \quad$ (Provided $\left. x \neq 0 \right)$

Question 2

Write a variation model. Use k as the constant of variation. W varies directly as h.

Accepted Answer

A)  $W = \frac { k } { h }$ 
B)  $W = k h$ 
C)  $W = \frac { e } { k }$ 
D)  $W = k + e$ 
A)  $W = \frac { k } { h }$ 
B)  $W = k h$ 
C)  $W = \frac { e } { k }$ 
D)  $W = k + e$

Question 3

The cost, in dollars, of filling your gas tank is directly proportional to the amount purchased. If 19 gallons of gas costs $26.60, how much would 22 gallons cost?

Accepted Answer

A)  $30.80 
B)  $29.60 
C)  $31.60 
D)  $13.57 
A)  $30.80 
B)  $29.60 
C)  $31.60 
D)  $13.57

Question 4

Find the least common denominator (LCD). $$\frac { 5 y + 3 } { 8 } , \frac { x ^ { 2 } } { 6 } , \frac { 7 } { 12 x }$$

Accepted Answer

A)  6 
B)  $12 x$ 
C)  $72 x$ 
D)  $24 x$ 
A)  6 
B)  $12 x$ 
C)  $72 x$ 
D)  $24 x$

Question 5

Solve the rational equation. $$\frac { 5 } { w } - \frac { 5 w - 10 } { w - 3 } = \frac { - 5 } { w - 3 }$$

Accepted Answer

The answer of Solve the rational equation. \[\frac { 5...

Question 6

The JUST-SAY-MOW lawn mowing company consists of two people: Lisa and Bob. If Lisa cuts the lawn by herself, she can do it in 3 hours. If Bob cuts the same lawn himself, it takes him an hour Longer than Lisa. How long would it take them if they worked together? Round to the nearest Hundredth of an hour.

Accepted Answer

A)  1.00 hour 
B)  3.50 hours 
C)  4.00 hours 
D)  1.71 hours 
A)  1.00 hour 
B)  3.50 hours 
C)  4.00 hours 
D)  1.71 hours

Question 7

A piece of manufacturing equipment can produce enough items to fill an order in 10 hours. If an auxiliary piece of equipment is used also, it will take 7 hours. How long would it take the auxiliary Equipment to fill the order working alone?

Accepted Answer

A)  3 hours 
B)  13 hours, 12 minutes 
C)  17 hours 
D)  23 hours, 20 minutes 
A)  3 hours 
B)  13 hours, 12 minutes 
C)  17 hours 
D)  23 hours, 20 minutes

Question 8

Multiply the rational expressions. $\frac { 3 x - 21 } { x } \cdot \frac { x ^ { 2 } + 3 x } { 7 x - 49 }$

Accepted Answer

A)  $\frac { 3 x ^ { 2 } + 9 x } { 7 x ^ { 2 } - 49 }$ 
B)  $\frac { 3 x ^ { 2 } - 63 } { 7 x - 49 }$ 
C)  $\frac { 3 ( x + 3 ) } { 7 }$ 
D)  $\frac { 7 ( x - 7 ) } { x }$ 
A)  $\frac { 3 x ^ { 2 } + 9 x } { 7 x ^ { 2 } - 49 }$ 
B)  $\frac { 3 x ^ { 2 } - 63 } { 7 x - 49 }$ 
C)  $\frac { 3 ( x + 3 ) } { 7 }$ 
D)  $\frac { 7 ( x - 7 ) } { x }$

Question 9

Find the constant of variation k.
y varies directly as x and when x = 9, y = 18

Accepted Answer

The answer of Find the constant of variation k.
y varies...

Question 10

Divide the rational expressions. $$\frac { 2 z - 3 } { z ^ { 3 } - 1 } \div \frac { 2 z ^ { 2 } + 5 z - 12 } { 5 z - 5 }$$

Accepted Answer

The answer of Divide the rational expressions. \[\frac { 2...

Question 11

Simplify the rational expression. $\frac { 9 x ^ { 2 } - 4 } { 4 - 6 x }$

Accepted Answer

A)  $- \frac { 3 x + 2 } { 2 }$ (Provided $\left. x \neq \frac { 2 } { 3 } \right)$ 
B)  $\frac { - 3 x + 2 } { 2 }$ (Provided $\left. x \neq \frac { 2 } { 3 } \right)$ 
C)  $\frac { 3 x + 2 } { 2 }$ (Provided $x \neq \frac { 2 } { 3 }$ ) 
D)  $\frac { 3 x } { 2 } \quad$ (Provided $\left. x \neq \frac { 2 } { 3 } \right)$ 
A)  $- \frac { 3 x + 2 } { 2 }$ (Provided $\left. x \neq \frac { 2 } { 3 } \right)$ 
B)  $\frac { - 3 x + 2 } { 2 }$ (Provided $\left. x \neq \frac { 2 } { 3 } \right)$ 
C)  $\frac { 3 x + 2 } { 2 }$ (Provided $x \neq \frac { 2 } { 3 }$ ) 
D)  $\frac { 3 x } { 2 } \quad$ (Provided $\left. x \neq \frac { 2 } { 3 } \right)$

Question 12

Solve the rational equation. $$\frac { z - 10 } { 5 } = \frac { z - 10 } { z }$$

Accepted Answer

The answer of Solve the rational equation. \[\frac { z...

Question 13

Perform the indicated operations. $$\frac { x ^ { 2 } + 3 x } { x - 1 } \div \frac { x ^ { 2 } - 9 } { 3 x - 3 } \cdot \frac { x - 3 } { x }$$

Accepted Answer

A)  $\frac { 1 } { 3 \left( x ^ { 2 } - 9 \right) }$ 
B)  3 
C)  $\frac { ( x + 3 ) ( 3 x - 3 ) } { x ( x - 3 ) }$ 
D)  $\frac { ( x + 3 ) ^ { 2 } ( x - 3 ) } { 3 ( x - 1 ) }$ 
A)  $\frac { 1 } { 3 \left( x ^ { 2 } - 9 \right) }$ 
B)  3 
C)  $\frac { ( x + 3 ) ( 3 x - 3 ) } { x ( x - 3 ) }$ 
D)  $\frac { ( x + 3 ) ^ { 2 } ( x - 3 ) } { 3 ( x - 1 ) }$

Question 14

Add or subtract as indicated and simplify if possible. $$\frac { t ^ { 2 } - 8 } { t - 3 } - \frac { - 4 t + 13 } { t - 3 }$$

Accepted Answer

A)  $\frac { t ^ { 2 } - 4 t + 5 } { t - 3 }$ 
B)  $t + 7$ 
C)  $\frac { t + 7 } { 2 }$ 
D)  $\frac { t ^ { 2 } + 4 t + 5 } { t - 3 }$ 
A)  $\frac { t ^ { 2 } - 4 t + 5 } { t - 3 }$ 
B)  $t + 7$ 
C)  $\frac { t + 7 } { 2 }$ 
D)  $\frac { t ^ { 2 } + 4 t + 5 } { t - 3 }$

Question 15

A boat can travel 56 miles upstream against the current in the same amount of time it can travel 84 miles downstream with the current. If the boat's average speed in still water is 20 miles per hour, find the speed of the current.

Accepted Answer

The answer of A boat can travel 56 miles upstream...

Question 16

Add. $$\frac { 8 } { 6 y ^ { 2 } } + \frac { - 9 } { 8 y }$$

Accepted Answer

A)  $\frac { - 27 y + 32 } { 24 y ^ { 2 } }$ 
B)  $\frac { - 1 } { 48 y ^ { 3 } }$ 
C)  $\frac { - 1 } { 14 y ^ { 3 } }$ 
D)  $\frac { 5 } { 24 y ^ { 2 } }$ 
A)  $\frac { - 27 y + 32 } { 24 y ^ { 2 } }$ 
B)  $\frac { - 1 } { 48 y ^ { 3 } }$ 
C)  $\frac { - 1 } { 14 y ^ { 3 } }$ 
D)  $\frac { 5 } { 24 y ^ { 2 } }$

Question 17

A plane can fly 540 miles with the wind in one hour less than it can fly 480 miles against the wind. The average wind speed is 30 miles per hour. Find the speed of the plane in still air.

Accepted Answer

A)  120 miles per hour 
B)  150 miles per hour 
C)  180 miles per hour 
D)  210 miles per hour 
A)  120 miles per hour 
B)  150 miles per hour 
C)  180 miles per hour 
D)  210 miles per hour

Question 18

Solve the proportion. $$\frac { y ^ { 2 } } { 6 } = \frac { 36 } { y }$$

Accepted Answer

The answer of Solve the proportion. \[\frac { y ^...

Question 19

Simplify the complex fraction by using Method I. $$\frac { \frac { 8 a } { 3 b ^ { 2 } } } { \frac { 6 a b } { 5 } }$$

Accepted Answer

A)  $\frac { 20 } { 9 b ^ { 3 } }$ 
B)  $\frac { 4 a } { 5 b ^ { 2 } }$ 
C)  $\frac { 9 b ^ { 3 } } { 20 }$ 
D)  $\frac { 16 a ^ { 2 } } { 5 b }$ 
A)  $\frac { 20 } { 9 b ^ { 3 } }$ 
B)  $\frac { 4 a } { 5 b ^ { 2 } }$ 
C)  $\frac { 9 b ^ { 3 } } { 20 }$ 
D)  $\frac { 16 a ^ { 2 } } { 5 b }$

Question 20

Simplify the complex fraction by using Method I. $$\frac { \frac { - 16 } { x ^ { 2 } } } { \frac { 10 } { 3 x } }$$

Accepted Answer

A)  $- \frac { 5 x } { 24 }$ 
B)  $- \frac { 26 } { x ^ { 2 } - 3 x }$ 
C)  $- \frac { 24 } { 5 x }$ 
D)  $- \frac { 160 } { 3 x ^ { 3 } }$ 
A)  $- \frac { 5 x } { 24 }$ 
B)  $- \frac { 26 } { x ^ { 2 } - 3 x }$ 
C)  $- \frac { 24 } { 5 x }$ 
D)  $- \frac { 160 } { 3 x ^ { 3 } }$

Simplify the rational expression. $\frac { 18 x ^ { 3 } y ^ { 6 } } { 45 x ^ { 5 } y ^ { 9 } }$

Write a variation model. Use k as the constant of variation. W varies directly as h.

The cost, in dollars, of filling your gas tank is directly proportional to the amount purchased. If 19 gallons of gas costs $26.60, how much would 22 gallons cost?

Find the least common denominator (LCD). $\frac { 5 y + 3 } { 8 } , \frac { x ^ { 2 } } { 6 } , \frac { 7 } { 12 x }$

Solve the rational equation. $\frac { 5 } { w } - \frac { 5 w - 10 } { w - 3 } = \frac { - 5 } { w - 3 }$

A piece of manufacturing equipment can produce enough items to fill an order in 10 hours. If an auxiliary piece of equipment is used also, it will take 7 hours. How long would it take the auxiliary Equipment to fill the order working alone?

Multiply the rational expressions. $\frac { 3 x - 21 } { x } \cdot \frac { x ^ { 2 } + 3 x } { 7 x - 49 }$

Find the constant of variation k. y varies directly as x and when x = 9, y = 18

Divide the rational expressions. $\frac { 2 z - 3 } { z ^ { 3 } - 1 } \div \frac { 2 z ^ { 2 } + 5 z - 12 } { 5 z - 5 }$

Simplify the rational expression. $\frac { 9 x ^ { 2 } - 4 } { 4 - 6 x }$

Solve the rational equation. $\frac { z - 10 } { 5 } = \frac { z - 10 } { z }$

Perform the indicated operations. $\frac { x ^ { 2 } + 3 x } { x - 1 } \div \frac { x ^ { 2 } - 9 } { 3 x - 3 } \cdot \frac { x - 3 } { x }$

Add or subtract as indicated and simplify if possible. $\frac { t ^ { 2 } - 8 } { t - 3 } - \frac { - 4 t + 13 } { t - 3 }$

A boat can travel 56 miles upstream against the current in the same amount of time it can travel 84 miles downstream with the current. If the boat's average speed in still water is 20 miles per hour, find the speed of the current.

Add. $\frac { 8 } { 6 y ^ { 2 } } + \frac { - 9 } { 8 y }$

A plane can fly 540 miles with the wind in one hour less than it can fly 480 miles against the wind. The average wind speed is 30 miles per hour. Find the speed of the plane in still air.

Solve the proportion. $\frac { y ^ { 2 } } { 6 } = \frac { 36 } { y }$

Simplify the complex fraction by using Method I. $\frac { \frac { 8 a } { 3 b ^ { 2 } } } { \frac { 6 a b } { 5 } }$

Simplify the complex fraction by using Method I. $\frac { \frac { - 16 } { x ^ { 2 } } } { \frac { 10 } { 3 x } }$

Linear Equations and Inequalities in One Variable

Linear Equations in Two Variables and Functions

Systems of Linear Equations and Inequalities

Polynomials

Radicals and Complex Numbers

Quadratic Equations, Functions and Inequalities

Exponential and Logarithmic Functions and Applications

Conic Sections

Binomial Expansions, Sequences, and Series

Online: Transformations, Piecewise-Defined Functions, and Probability

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Exam 5: Rational Expressions and Rational Equations

Simplify the rational expression. 18x3y645x5y9\frac { 18 x ^ { 3 } y ^ { 6 } } { 45 x ^ { 5 } y ^ { 9 } }45x5y918x3y6​

Write a variation model. Use k as the constant of variation. W varies directly as h.

The cost, in dollars, of filling your gas tank is directly proportional to the amount purchased. If 19 gallons of gas costs $26.60, how much would 22 gallons cost?

Find the least common denominator (LCD). 5y+38,x26,712x\frac { 5 y + 3 } { 8 } , \frac { x ^ { 2 } } { 6 } , \frac { 7 } { 12 x }85y+3​,6x2​,12x7​

Solve the rational equation. 5w−5w−10w−3=−5w−3\frac { 5 } { w } - \frac { 5 w - 10 } { w - 3 } = \frac { - 5 } { w - 3 }w5​−w−35w−10​=w−3−5​

A piece of manufacturing equipment can produce enough items to fill an order in 10 hours. If an auxiliary piece of equipment is used also, it will take 7 hours. How long would it take the auxiliary Equipment to fill the order working alone?

Multiply the rational expressions. 3x−21x⋅x2+3x7x−49\frac { 3 x - 21 } { x } \cdot \frac { x ^ { 2 } + 3 x } { 7 x - 49 }x3x−21​⋅7x−49x2+3x​

Find the constant of variation k. y varies directly as x and when x = 9, y = 18

Divide the rational expressions. 2z−3z3−1÷2z2+5z−125z−5\frac { 2 z - 3 } { z ^ { 3 } - 1 } \div \frac { 2 z ^ { 2 } + 5 z - 12 } { 5 z - 5 }z3−12z−3​÷5z−52z2+5z−12​

Simplify the rational expression. 9x2−44−6x\frac { 9 x ^ { 2 } - 4 } { 4 - 6 x }4−6x9x2−4​

Solve the rational equation. z−105=z−10z\frac { z - 10 } { 5 } = \frac { z - 10 } { z }5z−10​=zz−10​

Perform the indicated operations. x2+3xx−1÷x2−93x−3⋅x−3x\frac { x ^ { 2 } + 3 x } { x - 1 } \div \frac { x ^ { 2 } - 9 } { 3 x - 3 } \cdot \frac { x - 3 } { x }x−1x2+3x​÷3x−3x2−9​⋅xx−3​

Add or subtract as indicated and simplify if possible. t2−8t−3−−4t+13t−3\frac { t ^ { 2 } - 8 } { t - 3 } - \frac { - 4 t + 13 } { t - 3 }t−3t2−8​−t−3−4t+13​

A boat can travel 56 miles upstream against the current in the same amount of time it can travel 84 miles downstream with the current. If the boat's average speed in still water is 20 miles per hour, find the speed of the current.

Add. 86y2+−98y\frac { 8 } { 6 y ^ { 2 } } + \frac { - 9 } { 8 y }6y28​+8y−9​

A plane can fly 540 miles with the wind in one hour less than it can fly 480 miles against the wind. The average wind speed is 30 miles per hour. Find the speed of the plane in still air.

Solve the proportion. y26=36y\frac { y ^ { 2 } } { 6 } = \frac { 36 } { y }6y2​=y36​

Simplify the complex fraction by using Method I. 8a3b26ab5\frac { \frac { 8 a } { 3 b ^ { 2 } } } { \frac { 6 a b } { 5 } }56ab​3b28a​​

Simplify the complex fraction by using Method I. −16x2103x\frac { \frac { - 16 } { x ^ { 2 } } } { \frac { 10 } { 3 x } }3x10​x2−16​​

Linear Equations and Inequalities in One Variable

Linear Equations in Two Variables and Functions

Systems of Linear Equations and Inequalities

Polynomials

Radicals and Complex Numbers

Quadratic Equations, Functions and Inequalities

Exponential and Logarithmic Functions and Applications

Conic Sections

Binomial Expansions, Sequences, and Series

Online: Transformations, Piecewise-Defined Functions, and Probability

Filters

Simplify the rational expression. $\frac { 18 x ^ { 3 } y ^ { 6 } } { 45 x ^ { 5 } y ^ { 9 } }$

Find the least common denominator (LCD). $\frac { 5 y + 3 } { 8 } , \frac { x ^ { 2 } } { 6 } , \frac { 7 } { 12 x }$

Solve the rational equation. $\frac { 5 } { w } - \frac { 5 w - 10 } { w - 3 } = \frac { - 5 } { w - 3 }$

Multiply the rational expressions. $\frac { 3 x - 21 } { x } \cdot \frac { x ^ { 2 } + 3 x } { 7 x - 49 }$

Divide the rational expressions. $\frac { 2 z - 3 } { z ^ { 3 } - 1 } \div \frac { 2 z ^ { 2 } + 5 z - 12 } { 5 z - 5 }$

Simplify the rational expression. $\frac { 9 x ^ { 2 } - 4 } { 4 - 6 x }$

Solve the rational equation. $\frac { z - 10 } { 5 } = \frac { z - 10 } { z }$

Perform the indicated operations. $\frac { x ^ { 2 } + 3 x } { x - 1 } \div \frac { x ^ { 2 } - 9 } { 3 x - 3 } \cdot \frac { x - 3 } { x }$

Add or subtract as indicated and simplify if possible. $\frac { t ^ { 2 } - 8 } { t - 3 } - \frac { - 4 t + 13 } { t - 3 }$

Add. $\frac { 8 } { 6 y ^ { 2 } } + \frac { - 9 } { 8 y }$

Solve the proportion. $\frac { y ^ { 2 } } { 6 } = \frac { 36 } { y }$

Simplify the complex fraction by using Method I. $\frac { \frac { 8 a } { 3 b ^ { 2 } } } { \frac { 6 a b } { 5 } }$

Simplify the complex fraction by using Method I. $\frac { \frac { - 16 } { x ^ { 2 } } } { \frac { 10 } { 3 x } }$