Problem 89 - College Algebra

Question

Explain how to multiply rational expressions.

Step-by-Step Solution

Answer

To multiply rational expressions, write down the two rational expressions as a multiplication operation. Then, multiply the numerators together to get the new numerator and likewise for the denominators. Lastly, simplify the resulting rational expression to its simplest form.

Step 1: Setup the Multiplication

Assume two rational expressions \(\frac{a}{b}\) and \(\frac{c}{d}\). To multiply these rational expressions, write them close to each other like \(\frac{a}{b} \cdot \frac{c}{d}\).

Step 2: Multiply Numerators and Denominators

In this step, multiply the numerators together to create the new numerator and do the same with the denominators to get the new denominator. So \(\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}\).

Step 3: Simplify the Result

In this stage, it's often possible to simplify the resulting rational expression. Look for common factors in the numerator and the denominator that can be simplified or canceled out. For example, if after multiplication \(\frac{a \cdot c}{b \cdot d} = \frac{4x^2}{2x}\), it can be simplified to \(\frac{2x}{1}\) or just \(2x\).