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8.5 Solving Rational Equations

Learn how to solve rational equations with this step-by-step guide. Factor denominators, find the least common denominator (LCD), cancel out fractions, simplify, and solve for x. Includes examples.

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8.5 Solving Rational Equations

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  1. 8.5 Solving Rational Equations

  2. Steps to solve Rational Equations 1. Factor all denominators 2. Find the LCD • Multiply every term on both sides of the equation by the LCD to cancel out fractions 4. Simplify---no more fractions  5. Solve for x

  3. Example 1 LCD:

  4. Example 2 LCD:

  5. Example 3 LCD:

  6. = 3x + 4 5x x – 2 x – 2 Example 4 (x – 2) (x – 2) 5x = 3x + 4 2x = 4 No Solution x = 2 The solution x = 2 is extraneousbecause it makes the denominators of the original equation equal to 0. Therefore, the equation has no solution. 8-5 : Solving Rational Equations

  7. Example 5 8-5 : Solving Rational Equations

  8. Example 6 LCD:

  9. Example 7

  10. Example 8

  11. Example 9

  12. Example 10

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