8th Grade Math Unit 12 - Rational Expressions and Equations

Which graph could represent the following variation:

y varies inversely as x. y = 8 when x = - 5

Review Inverse Variations
1. A
2. B
3. C
4. D
Assume y varies inversely as x. Write an inverse variation equation that relates x and y, and solve:
If y = 8.2 when x = - 3.5, find x when y = - 0.5.

x = ________
Your Dad can drive 200 miles to the mountains in 4 hours if he can drive at an average speed of 50 miles per hour. Your sister says he can get there 20 minutes sooner if he can average 55 miles an hour without speeding.
Is she correct?
1. Yes
2. No
What is the constant of variation if y varies inversely as x, and y = - 5.45 when x = - 2.8

k = ________
What are all the excluded values of a rational expression if its denominator is x² + 6x - 27?

(Select all that apply.)

Review Rational Expressions
1. 0
2. - 9
3. 9
4. 3
5. - 3
Which of the following expressions is written in its simplest form?
1. A
2. B
3. C
4. D
In which expressions are 1 and 7 excluded values?
1. A
2. B
3. C
4. D
Your class is going to a celebration lunch. The bus will cost $250 and each lunch will cost $5. How many students must attend to keep the cost per student under $12.

_______ students
Find the product of:
1. 1 / (x² - 10x + 21)
2. 1 / (x² + 10x - 21)
3. 1 / (x² + 10x + 21)
4. ( x + 7 ) / (x² + 10x + 21)
Find the product:
1. ( b - 2 ) / ( b² - 16)
2. ( b + 2 ) / ( b² - 16)
3. ( b + 2 ) / ( b² + 16)
4. ( b + 2 ) / ( b - 16)
Check all the expressions below that are the equivalent of m/n:
1. (m + 4) / (n + 4)
2. a⁴m / a⁴n
3. (7 - m) / (7 - n)
4. m⁵ / n⁵
5. 4m/4n
Find the product of:

Review Rational Expressions
1. 3x² / (4x - 4)
2. 3x / (4x - 4)
3. x / (4x - 4)
4. 3x / (4x - 1)
Find the quotient of:
1. (x⁴ y z n)/ m
2. (x⁴ z n)/ m n
3. (x⁴ z n)/ m
4. (x³ z n)/ n
Find the quotient of:

Review Rational Expressions
1. (3x + 18) / ( x + 5)
2. (x + 5) / ( 3x + 18)
3. (3x + 15) / ( 3x + 18)
4. (x - 7) / ( 3x + 18)
Find the quotient when ( x - 9) / ( x + 5) is divided by x² - 8x - 9:
1. (x - 9) / (x + 1)
2. 1 / (x + 5) (x + 9)
3. (x - 9) / (x + 5)
4. 1 / (x + 5) (x + 1)
Find the quotient of:
1. (x² + 7x +12) / (x² -2x - 10)
2. (x² + x +12) / (x² -2x - 10)
3. (x + 4) / X - 5)
4. (x + 3) / (x + 2)
Find the width (W) of the following rectangle:

W = ______________
Using long division, find the quotient of 16b³ -32b² + 19b - 5 divided by 4b - 5:

Review Long Division of Rational Expressions
1. b² - 3b +1
2. 4b² + 3b +1
3. 4b² - 3b + 1
4. 4b² - 3b - 1
If b is an integer, and there is no remainder when x² + 8x + 12 is divided by x + b, what is the value of b?

b = ______
What is the remainder if you divide x³ + 7x - 30 by x - 5?
Find the difference between:

Review Adding and Subtracting Rational Expressions
Which expression below represents the perimeter of the following rectangle:
1. 15x
2. 5x / (x + 3y)
3. 10x / (x + 3y)
4. 30x / (x + 3y)
The following addition is correct::

Review Using LCM's in Rational Expressions
1. True
2. False
What is the least common denominator of:
1. (x - 2y) (x + 2y)
2. (x - 2y) (x + 2y)²
3. (x - 2y)² (x + 2y)
4. (x - 2y)² (x + 2y)²
Find:
1. (4x - 16) / (x -1) (x - 3)²
2. (4x - 16) / (x -1) (x - 3)
3. (x - 16) / (x -1) (x - 3)²
4. (4x - 16) / (x -1)² (x - 3)
Find the resulting denominator of the division of the following mixed expressions:
1. (x + 14) (x - 2) (x - 5)
2. (x + 12) (x + 7) (x - 2)
3. (x - 7) (x + 2)
4. (x + 12) (x - 7) (x + 2)
The following statement is correct:
1. True
2. False
Solve the follwing equation. Eliminate any extraneous solutions.

x = ________

Review Rational Equations
Which value is an extraneous solution to:

a = ___________
Solve the following equation. Eliminate any extraneous solutions.

m = _________