Question

Describe the steps used to multiply two rational expressions.

Short answer

To multiply two rational expressions, first factorize their numerators and denominators. Cross-cancel any common factors between them before multiplying the numerators together and the denominators together. Finally, simplify the result if necessary.

Step-by-step solution

Understand the Expression

Write down the two rational expressions that are to be multiplied. Each expression will have a numerator and a denominator which are both polynomials.

Factorize Numerators and Denominators

Factorize the numerator and the denominator for each of the rational expressions. Expand them out into their simplest polynomial expressions.

Cross Cancelation

Look for common factors between the numerators and denominators. These can be cross-cancelled. If factor A is in the numerator and denominator of the expressions, simplify by dividing each by factor A.

Perform Multiplication

Practice the actual multiplication. Multiply the remaining factors in the numerator to get the numerator of the resulting expression, and do the same thing for the denominator.

Simplify

Check if there are any common factors left between the numerator and denominator. If yes, simplify by dividing each by that common factor. If not, the expression is already simplified. Write down the resulting rational expression.