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Rational Equations Section 8-6

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

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

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**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

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Today Cross Multiplying Method

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**Cross Multiplication Method**

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Example 2

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Example 3

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**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

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Homework WS 12-5

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