Question

Task 4—Solving Rational Equations

Using the equation below as a model, fill in numbers in the place of a and b to create a rational equation that has an extraneous solution.

x + a (over(fraction)) ax = b (over(fraction)) x

Part 1. Show all work to solve for x in the equation and check the solution.

Part 2. Explain how to identify the extraneous solution and what it means.

Answer 1

Explanation:

Using the equation below as a model, fill in numbers in the place of a and b to create a rational equation that has an extraneous solution.

X + 4 / 4x = 8 / x

Part 1. Show all work to solve for x in the equation and check the solution.

X + 4 / 4x = 8 / x

x(x + 4) = (4x)8

x^2 + 4x = 32x

x^2 + 4x - 32x = 32x - 32x

x^2 - 28x = 0

x(x - 28) = 0

X = 0 or x = 28

Part 2. Explain how to identify the extraneous solution and what it means.

The solution x = 0 is extraneous because you are not allowed to divide by 0.

Answer 2

x = 7 is a solution

x = -2 is an extraneous solution.

Explanation: