Problem 78 - Introductory Algebra for College Students

Question

Explain how to divide rational expressions.

Step-by-Step Solution

Answer

To divide rational expressions, first find the reciprocal of the second fraction. Then, convert the operation from division to multiplication and perform the multiplication. Simplify the result if possible after the multiplication.

Step 1: Identify the Rational Expressions

The first step is to identify the rational expressions that you want to divide. They should be in the form \( \frac{Numerator1}{Denominator1} \div \frac{Numerator2}{Denominator2} \).

Step 2: Find the Reciprocal of the Second Fraction

Next, find the reciprocal of the second fraction. The reciprocal of a fraction is obtained by exchanging the roles of the numerator and the denominator. It would change \( \frac{Numerator2}{Denominator2} \) into \( \frac{Denominator2}{Numerator2} \).

Step 3: Convert Division into Multiplication

Change the division operation into a multiplication operation. Division by a fraction is the same as multiplication by its reciprocal. Your problem should now look like this: \( \frac{Numerator1}{Denominator1} \times \frac{Denominator2}{Numerator2} \).

Step 4: Perform the Multiplication

Now you can perform the multiplication. When multiplying, you multiply the numerators together to form the new numerator and the denominators together to form the new denominator. The product should yield \( \frac{Numerator1 \times Denominator2}{Denominator1 \times Numerator2} \).

Step 5: Simplification

Finally, simplify the result if possible. Factors present in both the numerator and the denominator can be cancelled out. Always express your final answer in simplified form.