Question

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 plus a over ax = b over 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

Lets solve the equation step by step:

(x + a)/ax = b/x

therefore: a != 0, x !=0

now we solve:

(x + a)/ax = b/x
(x + a)/a = b
x + a = ab
x = a(b - 1)

that is the solution for b, and we keep in mind that a != 0, x !=0, the extraneous solutions