AnswersAlgebra II - MA3111 A-CRAdding and Subtracting Rational Expressions

Rational Equations Answers

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1
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A student solves the following equation for all possible values of x:His solution is as follows: Step 1: 8(x – 4) = 2(x + 2)Step 2: 4(x – 4) = (x + 2)Step 3: 4x – 16 = x + 2Step 4: 3x = 18Step 5: x = 6He determines that 6 is an extraneous solution because the difference of the numerators is 6, so the 6s cancel to 0.Which best describes the reasonableness of the student’s solution?

Question illustration
A
His solution for x is correct and his explanation of the extraneous solution is reasonable.
B
His solution for x is correct, but in order for 6 to be an extraneous solution, both denominators have to result in 0 when 6 is substituted for x.
C
His solution for x is correct, but in order for 6 to be an extraneous solution, one denominator has to result in 0 when 6 is substituted for x.
D
His solution for x is incorrect. When solved correctly, there are no extraneous solutions.
2
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Which solution to the equation is extraneous?

Question illustration
A
g = –4
B
g = –4 and g = 16
C
neither g = –4 nor g = 16
D
g = 16
3

What is the solution to the equation ?

Question illustration
A
m = 3
B
m = 6
C
all real numbers
D
no solution
4

Which solution to the equation is extraneous?

Question illustration
A
x = 1 and x = –4
B
neither x = 1 or x = –4
C
x = 1
D
x = –4
5

Kent multiplies both sides of the equation below by an expression.Then he moves all the terms to one side of the equal sign in the resulting equation. Which equation must he solve now?

Question illustration
A
k squared minus 8 k minus 12 = 0
Option A
B
k squared + 8 k + 12 = 0
Option B
C
k squared minus 8 + 12 = 0
Option C
D
k squared minus 8 k + 12 = 0
Option D
6

What causes a solution to a rational equation to be an extraneous solution?

A
When there is more than one solution, one of the solutions is extraneous.
B
If a solution results in zero when substituted into the denominator of the equation, the solution is extraneous.
C
If a solution results in a negative number when substituted into the denominator of the equation, the solution is extraneous.
D
When a solution is a fraction, the solution is extraneous.
7

Janet wants to solve the equation . What should she multiply both sides of the equation by?

Question illustration
A
y
B
y2 – 1
C
y + 1
D
y2 + y + 2
8

Yumi and Juan pick up litter along the highway at the same rate. Yumi picks up litter for 3 miles and takes 2 hours longer than Juan, who picks up litter for 2 miles. If Juan spent x hours picking up litter, the following equation models the situation.How long did Yumi spend picking up litter?

Question illustration
A
1 hour 20 minutes
B
3 hours 20 minutes
C
4 hours
D
6 hours
9

Which of the following represents the solution of ?

Question illustration
A
x = one-fifth
Option A
B
x = five-ninths
Option B
C
all real numbers
D
no solution
10

What are the solutions to the equation ?

Question illustration
A
w = –6 and w = –2
B
w = 0, w = 2, and w = 6
C
w = 0 and w =
Option C
D
w = 2 and w = 6

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Rational Equations Answers — Algebra II - MA3111…