1. Table of Contents Add & Subtract Rationals – Unlike Denominators It is assumed that you understand the material in the three previous modules: 1) Addition and subtraction of rational expressions with common denominators 2) Finding the LCM of two expressions 3) Writing equivalent rational expressions

2. Table of Contents To add or subtract rational expressions with unlike denominators: 1) Determine the LCD (LCM of the denominators) 2) Write each rational expression as an equivalent rational expression with the LCD as its denominator 3) Add or subtract as you did with common denominators

3. Table of Contents Example 1 Determine the LCD Add the two rational expressions Note that the denominators are not common

4. Table of Contents Write each rational as an equivalent expression with the LCD

5. Table of Contents Write each rational as an equivalent expression with the LCD

6. Table of Contents Write each rational as an equivalent expression with the LCD for the denominator

7. Table of Contents Add the equivalent rational expressions that now have a common denominator

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9. Since we can’t factor the numerator and nothing can reduced, this is the answer.

10. Table of Contents Example 2 In the last problem, we went to great detail to find the equivalent rational expressions. Here is a shorter version of the same problem. Add the two rational expressions Determine the LCD

11. Table of Contents Write the equivalent rational expressions

12. Table of Contents Since we can’t factor the numerator and nothing can be reduced, this is the answer.

13. Table of Contents Example 3 Subtract the two rational expressions Note that the denominators are not common Determine the LCD

14. Table of Contents Write the equivalent rational expressions

15. Table of Contents Since we can’t factor the numerator and nothing can be reduced, this is the answer.

16. Table of Contents Example 4 Subtract the two rational expressions Note that the denominators are not common Determine the LCD

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18. Be careful of the sign here

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