Multiplying Rational Expressions Use the following steps to multiply rational expressions. 1.Factor each numerator and denominator. 2.Reduce factors that are common to both a numerator and a denominator. 3.Multiply numerators. 4.Multiply denominators.

Example 1 Factor the denominator on the left. Reduce common factors. Multiply The simplified product is …

Example 2 Factor all numerators and denominators Multiply Sometimes the reducing is simpler if a squared factor is written as a product.

Reduce common factors. The simplified product is …

Note that in this last problem we reduced a common factor (x+4) found in different rational expressions … … and reduced a common factor (x+4) found in the same rational expression.

The important thing here is to reduce a common factor in one numerator and one denominator. It doesn’t make any difference which rational expression they come from.

Example 3 There is nothing to factor on this problem. Notice that both numerators have a common variable x. Multiply When this happens, it is usually easier to multiply the numerators first. Do this with both numerators and denominators.

Reduce common factors. Note that it was convenient to leave the numerical coefficients in factored form. The simplified product is …