AnswersPARTA - EVP PGCPS ALGEBRA 2 OC FALL2026 - 793033Multiplying and Dividing Rational Expressions

Rational Equations Answers

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1
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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
2
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What is true about the solution of ?

Question illustration
A
, and they are actual solutions.
Option A
B
, but they are extraneous solutions.
Option B
C
x = 3, and it is an actual solution.
D
x = - 3, but it is an extraneous solution.
3

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
4

What is the solution to the equation ?

Question illustration
A
d = –4 and d = 2
B
d = –2 and d = 4
C
d = 1
D
d = 2
5

Working alone, it would take Shandra 40 minutes to sand a table. To sand the same table, also working alone, it would take Kelly 1 hour. If they work together, the situation can be modeled by the following equation, where t is the time it would take to sand the table working together.Shandra claims it will take them about 50 minutes working together, because 50 is the mean of 40 and 60. Which best describes Shandra’s claim?

Question illustration
A
Shandra’s claim is correct.
B
Shandra’s estimate is too high because she should have found the differences instead of the mean.
C
Shandra’s estimate is too high because it will take them about 24 minutes.
D
Shandra’s estimate is too low because it will take them about 100 minutes.
6

What is the solution for the equation ?

Question illustration
A
b = –4 and b = 0
B
b = –4
C
b = 0 and b = 4
D
b = 4
7

What are the solutions to the equation

Question illustration
A
x = –7 and x = 1
B
x = –6 and x = –1
C
x = –1 and x = 7
D
x = 1 and x = 6
8

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.
9

What is the solution of ?

Question illustration
A
y = –4
B
y = –2
C
y = 4
D
y = 6
10

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
11

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.
12

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
13

What is the solution of ?

Question illustration
A
y = –4
B
y = –2
C
y = 4
D
y = 6
14

What is the solution to the equation ?

Question illustration
A
m = 3
B
m = 6
C
all real numbers
D
no solution
15

What is the solution to the equation ?

Question illustration
A
d = –4 and d = 2
B
d = –2 and d = 4
C
d = 1
D
d = 2
16

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
17

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
18

Consider the graph showing two functions. Which answer can be used to find the solution to the system of equations?

Question illustration
A
mc030-2.jpg
Option A
B
mc030-3.jpg
Option B
C
mc030-4.jpg
Option C
D
mc030-5.jpg
Option D
19

What is true about the solution of ?

Question illustration
A
, and they are actual solutions.
Option A
B
, but they are extraneous solutions.
Option B
C
x = 3, and it is an actual solution.
D
x = - 3, but it is an extraneous solution.
20

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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