Multiplying Rational Functions

Remember that a rational function is one represented as a fraction. Multiply rational functions by following the usual procedure for multiplying any fraction:

Step 1) Multiply the numerator by the other numerator using FOIL Method.

Step 2) Multiply the denominator by the other denominator using FOIL Method.

Step 3) Reduce/simplify the fraction (if needed)

Example A:

$$ \frac{x+1}{x+3}*\frac{2x+3}{x-1} $$

Start by multiplying the numerators first:

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

Now multiply the denominators:

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

Final answer:

$$ \frac{2x^2 + 5x + 3}{x^2 + 2x - 3} $$

Example B:

$$ \frac{x^2 - 4}{x - 3}*\frac{x^2 - 7x + 12}{x^2 - 2x} $$

Step 1) Multiply numerators:

$$ (x^2-4)(x^2-7x+12) = x^4-7x^3+8x^2-28x-48 $$

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