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Efficient Solutions to Rational Equations

Learn an efficient approach to solving rational equations by multiplying through with the LCD and avoiding extraneous solutions. Practice with examples and shortcuts provided. Check your answers for accuracy.

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Efficient Solutions to Rational Equations

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  1. 8.6 Solving Rational Equations pg.570

  2. Hint for solving: • A quick way to solve a rational equation is to multiply everything through by the LCD. • This will get rid of all the fractions! • Beware of extraneous solutions!

  3. Example: Solve. LCD: 2x Multiply each fraction through by the LCD

  4. Solve. LCD: ? LCD: (x+1)

  5. Solve. Factor 1st! LCD: (x+2)(x-2)

  6. Short Cut! When there is only fraction on each side of the =, just cross multiply as if you are solving a proportion.

  7. Example: Solve.

  8. Last Example: Solve. Check your solutions!

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