Lesson 2-5

Refresher Simplify the following expressions

Multiplying Rational Expressions  The objective is to be able to multiply rational expressions.

Multiplying Rational Expressions We multiply rational expressions the same way that we multiply fractions. Example: multiply Step 1: Multiply the numerators: 36x 2 __ 316x 5 Step 2: Multiply the denominators: 36x 2 48x 5

Multiplying Rational Expressions Step 3: Find the greatest common factor (GCF) of the numerator and denominator: the GCF of 36x 2 and 48x 5 is 12x 2. Step 4: Factor the GCF out of both the numerator and the denominator: 12x 2 3_ 12x 2 4x 3 Step 5: Simplify your expression: : 3_ 4x 3

Method 2 Write the prime factorization of all parts of each fraction. Multiply them together but don’t simplify. Remove any sets in the numerator and denominator that divide to 1. Multiply the numerator and denominator to find the simplified rational. Example:

Example 2

Let’s Practice Multiply the following rational expressions. Make sure that your answer is in simplified form.

Dividing Rules When we are dividing rational expressions, we follow the same rules as dividing fractions. We find the reciprocal of the divisor (the 2 nd term) and multiply. Example: 2x + 4 ÷ x + 2 5x 3 2x 2 Take the reciprocal of the divisor. x + 2 → 2x 2 _ 2x 2 x + 2 Multiply: 2x + 4 2x 2 _ 5x 3 x + 2

Reciprocal Find the reciprocal of: 1 x + 2 1

Example 16x 2 4x 2 8x 16x 16x 2 16x 8x 4x x x 4 4 x 8 1 x 4 1 x x ÷

Example 2

Let’s Practice 5 3 5x 20x 2 2x x y 3 y ÷ ÷