1. Be sure to check all solutions for extraneous roots!

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. 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. Multiply each fraction by the lowest common denominator. 2 3 3x 5 x 3x 7 x    3x 

5. Simplify

6. 15    221x Subtract 15 from each side of the equation.. 26x 

7. Divide each side of the equation by 2. 2 2 6 2 3 x x   Simplify. Be sure to check in original equation (above)….. 5/3 + 2/3 = 7/3 yes!

8. SOLUTION Note-it’s a good idea to put a ” 1” under any Part that is not a fraction already

9. M=140/3 Multiply by the lowest common denominator. 15 1 5 4 3 8 mm m m m  Divide out common factors. Simplify Solve 3m-20=120

10. Multiply by the lowest common denominator Divide out common factors. Simplify

11. Solve a = 1 or -3 Check each one!

12. Check: 1 and -3 They both check

13. Solution to 3

14. The previous examples 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. Extraneous roots can be found by graphing the function-see problems 20-22 in the textbook on page 255. They can also be irrational (see problem 23 on the same page).