Problem 90 - College Algebra Essentials

Question

Explain how to divide rational expressions.

Step-by-Step Solution

Answer

To divide rational expressions: 1) Factor the numerators and denominators, 2) Change the division to multiplication by finding the reciprocal of the second fraction, 3) Multiply the numerators and denominators, 4) Simplify the result if any common factors exist.

Step 1: Factor the Numerator and Denominator

The main goal here is to simplify the expressions. To do this, start by factoring both the numerator and denominator of each fraction. Factoring helps reveal shared factors in the numerator and denominator, which can then be canceled out to simplify the expression.

Step 2: Rewrite Division as Multiplication

Division of rational expressions can be tricky, but not if it's transformed into a multiplication problem. This is done by finding the reciprocal of the second fraction and then changing the operation from division to multiplication. To find the reciprocal, switch the numerator and denominator of the fraction. Now, instead of dividing by the second fraction, you will multiply by its reciprocal.

Step 3: Multiply Numerators and Denominators

After converting the division problem into a multiplication one, now multiply the numerators together to get the new numerator and the denominators together to get the new denominator.

Step 4: Simplify the Expression

After multiplication, check if there are any common factors in the numerator and denominator of the result. If there are, cancel them out. If no further simplification is possible, write the final answer. If the denominator of the answer is 1, we usually write the answer as the numerator-only.