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Solving Rational Equations: Methods and Solutions

Learn to solve rational equations by finding the lowest common denominator and applying appropriate methods and techniques. Practice various problems to enhance your understanding.

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Solving Rational Equations: Methods and Solutions

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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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