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Joyce DuVall Green Valley High School Henderson, Nevada

Solving Rational Equations. Joyce DuVall Green Valley High School Henderson, Nevada. Objective and Vocabulary. The objective is to be able to solve rational equations. Lowest Common Denominator (LCD) – The smallest denominator which has all of the original denominators as factors.

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Joyce DuVall Green Valley High School Henderson, Nevada

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  1. Solving Rational Equations Joyce DuVall Green Valley High School Henderson, Nevada

  2. Objective and Vocabulary • The objective is to be able to solve rational equations. • Lowest Common Denominator (LCD) – The smallest denominator which has all of the original denominators as factors.

  3. Method 1 Step 1 – Find the lowest common denominator for the fractions. The lowest common multiple of 3 and x is 3x. Therefore, the LCD is 3x.

  4. 5 2 7 3 x 3 x 3 x x 3 x Step 2 Multiply each fraction by the lowest common denominator. + · · = ·

  5. Step 3 Simplify

  6. Step 4 + = 15 2 x 21 Subtract 15 from each side of the equation.. - - 15 15 = 2 x 6

  7. Step 5 Divide each side of the equation by 2. 2 x 6 = 2 2 Simplify. = x 3

  8. SOLUTION You Try It

  9. Problem 1 1 4 8 Multiply by the lowest common denominator. · - · = · 15 m 15 m 15 m 5 3 m m Divide out common factors. Simplify Solve

  10. Problem 2 Multiply by the lowest common denominator Divide out common factors. Simplify

  11. Problem 2 Solve

  12. Method 2 The previous example had two or more fractions on one side of the equation. When there is a single fraction on each side of the equation, the equation can be solved as a proportion by cross-multiplying.

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