Problem 74 - College Algebra

Question

Explain how to divide rational expressions.

Step-by-Step Solution

Answer

To divide rational expressions, the operation is changed to multiplication by taking the reciprocal of the second expression and then multiplying the expressions. The result is simplified by canceling common factors to give the simplest terms.

Step 1: Recognize Division as Multiplication by Reciprocal

Understand that dividing by a rational expression is the same as multiplying by its reciprocal. A reciprocal of a fraction is obtained by swapping its numerator and denominator.

Step 2: Write the Multiplication Expression

Rewrite the division operation as multiplication by writing the first rational expression times the reciprocal of the second expression.

Step 3: Multiply the Rational Expressions

To multiply two fractions (or rational expressions), multiply the numerators to get a new numerator, and multiply the denominators to get a new denominator.

Step 4: Simplify the Expression

Simplify the result from Step 3. This may involve factoring the numerator and denominator and canceling common factors. Leave the expression in simplest terms.