Rational equations

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 plus a all over ax = b over x (x + a/ax = b/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

Multiply both sides of the equation by ax to remove the denominators

so x + a = ab

then subtract a on both sides of the equation

now x = ab - a

next factor

x = a(b - 1)

if a = 0 then zero would be an extraneous solution because a is in the denominator of the original equation.

Also if b = 1 then 1 would also be an extraneous solution because x would equal zero and x is also in the denominator of the original equation.