# Multiplication of Rational Functions

How to multiply rational functions:

1) multiply the numerator by numerator using FOIL Method
2) multiply denominator by denominator using FOIL Method
3) reduce the fraction (if needed)

Sample A:

(x + 1)/(x + 3) TIMES (2x + 3)/(x - 1)

I will multiply the numerators first.

(x + 1) (2x + 3) = 2x^3 + 5x + 3

I will now multiply the denominators.

(x + 3) ( x - 1) = x^2 + 2x -3

Final answer: 2x^3 + 5x + 3/x^2 + 2x - 3

Sample B:

x^2 - 4/x - 3 TIMES x^2 - 7x + 12/x^2 - 2x

1) Factor where needed.

(x + 2) (x - 2)/x - 3 and (x - 3) ( x - 4)/x(x - 2)

2) Cancel where you can.

We can cancel the following: (x - 3) with (x - 3) and (x - 2) with (x - 2).

After doing so, we are left with the final answer: (x + 2) ( x - 4)/x

You can leave the final answer as shown above (called factored form) or you can write your final answer in standard form by multiplying to simplify.

Look at the difference:

Factored Form For Sample B

(x + 2) ( x - 4)/x

Standard Form For Sample B

x^2 - 2x - 8/x

By Mr. Feliz
(c) 2005