Solving Rational Equations

1. Solving Rational Equations Lesson 4

2. Objectives • Find the values that will make a rational expression undefined(excluded values) • Solve rational equations

3. Algebraic Fraction/Rational Expression Since a RE indicates division, we cannot replace the variables in a denominator with numbers that make the denominator zero.

4. State the value of the variable that will make the expression undefined.

5. State the value of the variable that will make the expression undefined.

6. State the value of the variable that will make the expression undefined.

7. State the value of the variable that will make the expression undefined.

8. Recall: Find the LCD

9. Recall: Find the LCD

10. Recall: Find the LCD

11. Solving Rational Equations • Identify and exclude any values that will make the denominator zero. • Multiply both sides by the LCD and simplify (this will eliminate all denominators). • Solve the resulting equation. • Check all solutions in the original equation.

12. Example 12Solve the equation.

13. Multiply by the LCD: 15

14. Example 13Solve the equation.

15. Example 13 multiply by LCD. Simplify – denominators are eliminated Distribute Solve for b. Check: We need 2b – 5 ≠ 0 and b – 3 ≠ 0 which means b ≠ 5/2 and b ≠ 3.

16. Solve for m. Since m2- m = m(m – 1), the LCD is m(m – 1), where m≠0 and m ≠ 1.

17. Solve for m. multiply by LCD. Simplify – denominators are eliminated Distribute Solve for m. 2(m – 1) – m = 4 2m - 2 - m = 4 m = 6

18. Solve for x. multiply by LCD. x2 – 3x + 12 = x – 3 + 4x x2 – 8x + 15 = 0 (x – 3)(x – 5) = 0 x = 3 or x = 5 Simplify – denominators are eliminated Set equation equal to zero. Factor. Zero factor property x = 3 is an extraneous root and x =5 is the only solution.

19. SOLVING RATIONAL EQUATIONS • Find the LCD • Multiply both sides of the equation by the LCD. • Solve using APE/MPE and/or • Solve by factoring. • Cross check solutions with restrictions

20. Solve for x.

21. Solve for y.