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

Rational Equations Answers

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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?

k squared minus 8 k minus 12 = 0

k squared + 8 k + 12 = 0

k squared minus 8 + 12 = 0

k squared minus 8 k + 12 = 0

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Which solution to the equation is extraneous?

x = 1 and x = –4

neither x = 1 or x = –4

x = 1

x = –4

What are the solutions to the equation ?

w = –6 and w = –2

w = 0, w = 2, and w = 6

w = 0 and w =

w = 2 and w = 6

What is the solution to the equation ?

m = 3

m = 6

all real numbers

no solution

A contractor has two choices for billing a completed job. · $500 flat rate, regardless of the number of hours worked· $20 per hour workedThe graph shows the relationship between pay per hour and number of hours worked for both scenarios. What is the solution to this system of equations, and what does it mean to the contractor?

The solution (0, 20) tells the contractor the minimum amount that can be charged.

The solution (0, 500) tells the contractor the maximum amount that can be charged.

The solution (25, 20) tells the contractor the number of hours on a job where the hourly rate is the same for both billing options.

The solution (20, 25) tells the contractor the number of hours on a job where the hourly rate is the same for both billing options.

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

y2 – 1

y + 1

y2 + y + 2

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?

His solution for x is correct and his explanation of the extraneous solution is reasonable.

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.

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.

His solution for x is incorrect. When solved correctly, there are no extraneous solutions.

What is the solution for the equation ?

b = –4 and b = 0

b = –4

b = 0 and b = 4

b = 4

What is the solution of ?

y = –4

y = –2

y = 4

y = 6

What is the solution to the equation ?

d = –4 and d = 2

d = –2 and d = 4

d = 1

d = 2

How many extraneous solutions does the equation below have?

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?