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Section 6.4

Section 6.4. Rational Equations. Objectives. Solving Rational Equations Solving an Equation for a Variable.

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Section 6.4

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  1. Section 6.4 • Rational Equations

  2. Objectives Solving Rational Equations Solving an Equation for a Variable

  3. One way to solve a rational equation is to clear fractions by multiplying each side of the equation by the least common denominator (LCD). When solving a rational equation, always check your answer.

  4. Example Solve each equation and check your answer. Start by determining the LCD, which is 4x. Check:

  5. Example Solve each equation and check your answer. Start by determining the LCD, which is (x + 3)(x – 3). or

  6. Example (cont) Solve each equation and check your answer. Check: We know that the equation is undefined when x = 3. We check the only possible solution x = −2. The only solution is −2.

  7. Example Solve graphically. Solution Graph and (1, 1) (−2, −2) The solutions are −2 and 1.

  8. Example Solve each equation. a. b. Solution a. b. The answer checks. Therefore the solution is –4/3. The answer checks. Therefore the solution is −4.

  9. Example Solve the equation. Solution Both solutions check.

  10. Example Solve the equation. Solution The LCD is (x + 2)(x – 1). Note that 0 – 1 and 1 cannot be solutions.

  11. Example Both solutions check.

  12. Example A pump can fill a swimming pool ¾ full in 6 hours, another can fill the pool ¾ full in 9 hours. How long would it take the pumps to fill the pool ¾ full, working together? Solution The two pumps can fill the pool ¾ full in hours.

  13. Example Solve the equation for the specified variable. Solution

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