How do you multiply polynomial fractions?

To multiply polynomial fractions, also called rational expressions, break down the given problem into individual polynomials, and factor them. Once the polynomials are factored, cancel any like factors, and simplify the remainder. Do not make the mistake of canceling similar terms between the fractions.

1. Factor all of the polynomials

   Factor the polynomials in both fractions of the problem. If given the expression, ((x^2 + 2x - 3) / (2x^2 + 2x - 4)) * ((x^2 + 7x + 10) / (x^2 + 4x + 3)), factor out both the numerator and the denominator. It is possible to multiply out the polynomials without factoring them; however, this makes simplification very difficult.

2. Cancel any like terms

   Once the expression is factored out to resemble (((x + 3) * (x - 1)) / (2 * (x - 1) * (x + 3))) * (((x + 2) * (x + 5)) / ((x + 1) * (x + 3))), cancel any like terms. Cancellation is valid between the numerator and denominator of the same fraction and between fractions. Cancellation cannot occur between the two numerators or the two denominators.

3. Simplify the expression

   After cancellation, the expression is easier to work with. Multiply out the remaining terms to determine the product of the expression: (x + 5) / (2 * (x + 1)) = (x + 5) / (2x + 2).