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Rational Expressions Chapter 8

8 Rational Expressions 8.1 Simplifying Rational Expressions 8.2 Multiplying and Dividing Rational Expressions 8.3 Finding the Least Common Denominator 8.4 Adding and Subtracting Rational Expressions Putting It All Together 8.5 Simplifying Complex Fractions 8.6 Solving Rational Equations 8.7 Applications of Rational Equations

8.2 Multiplying and Dividing Rational Expressions Multiply Fractions We multiply rational expressions the same way we multiply rational numbers. Multiply numerators, multiply denominators, and simplify. Let’s review with multiplication of two fractions. Multiply Fractions Example 1 Solution We can multiply numerators, multiply denominators, then simplify by dividing out common factors, or we can divide out the common factors before multiplying. Factor and divide out common factors. Multiply. Simplify.

Multiply Rational Expressions Example 2 Notice that Solution Factor and reduce. Notice that . was written as so that you will be able to cancel out the term. Multiply.

Example 3 Solution Factor and reduce. Multiply.

Example 4 Solution Factor and reduce. Multiply.

Divide Rational Expressions When we divide rational numbers, we multiply by a reciprocal. For example, .We divide rational expressions the same way. To divide rational expressions, we multiply the first rational expression by the reciprocal of the second rational expression. 2 1

Example 5 Solution 6 1 Get reciprocal. Multiply by reciprocal and reduce. 1 Multiply. Change division to multiplication.

Example 6 Solution Get reciprocal. Multiply by reciprocal and reduce. Change division to multiplication. Multiply.

Example 7 Solution Multiply by reciprocal and reduce. Factor out a -1.

Example 8 Solution Multiply by reciprocal and reduce. 3 2 Multiply.