 # Rational Equations Section 8-6.

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Rational Equations Section 8-6

Objectives Solve rational equations with one variable by CROSS MULTIPLYING Check answers for Extraneous Solutions

Extraneous Solutions Any solution that makes a denominator ZERO does not check. (Extraneous)

Solving Rational Equations
Two basic methods 1. Cross Multiply two rational expressions to solve them 2. Set equation equal to ZERO and then get Common Denominator

Today Cross Multiplying Method

Cross Multiplication Method

Example 2

Example 3

Solve a rational equation by cross multiplying
EXAMPLE 1 Solve a rational equation by cross multiplying Solve: 3 x + 1 = 9 4x + 1 3 x + 1 = 9 4x + 1 Write original equation. 3(4x + 5) = 9(x + 1) Cross multiply. 12x + 15 = 9x + 9 Distributive property 3x + 15 = 9 Subtract 9x from each side. 3x = – 6 Subtract 15 from each side. x = – 2 Divide each side by 3. The solution is –2. Check this in the original equation. ANSWER

Homework WS 12-5