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.
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.
Part 3. Use complete sentences to explain how the remainder theorem is used to determine whether your linear binomial is a factor of your polynomial function.

Answer 1

$\frac{x+a}{ax} = \frac{b}{x}$

for a=1 and b=2 =>

$\frac{x+1}{x} = \frac{2}{x}$

We have to cross multiply to get:
x(x+1) = 2x
x^2 + x = 2x
x^2 -x = 0
x(x-1)=0
x=0 or x=1

The x=0 solution is extraneous because we are not allowed to divide by 0 (which is what happens in the original equation if x is 0).