1. Simplify Rational Algebraic Expressions In the previous section on polynomials, we divided a polynomial by a binomial using long division. In this section, we will use the factoring methods to simplify rational expressions.

2. Simplify Rational Algebraic Expressions In the previous section on polynomials, we divided a polynomial by a binomial using long division. In this section, we will use the factoring methods to simplify rational expressions. A rational expression is simply a fraction that has polynomial expressions contained in the numerator and denominator…and the denominator can not equal zero

3. Simplify Rational Algebraic Expressions

4. I started you off with a simple one to get us started…

5. Simplify Rational Algebraic Expressions STEP #1 : FACTOR all expressions completely

6. Simplify Rational Algebraic Expressions

8. STEP #1 : FACTOR all expressions completely STEP # 2 : Look for COMMON FACTORS to “cancel”

9. Simplify Rational Algebraic Expressions

12. WARNING !!!

13. Simplify Rational Algebraic Expressions WARNING !!! You CAN NOT start by dividing individual terms to simplify…

14. Simplify Rational Algebraic Expressions WARNING !!!

15. Simplify Rational Algebraic Expressions WARNING !!!

16. Simplify Rational Algebraic Expressions WARNING !!!

17. Simplify Rational Algebraic Expressions WARNING !!!

18. Simplify Rational Algebraic Expressions WARNING !!!

19. Simplify Rational Algebraic Expressions WARNING !!! So as a general rule, if you see + / - signs separating terms, you must factor to get common terms to simplify. You can only cancel multiplied terms.

20. Simplify Rational Algebraic Expressions

21. STEP #1 : FACTOR all expressions completely

22. Simplify Rational Algebraic Expressions STEP #1 : FACTOR all expressions completely Factors of 4 that add/subtract = - 3 are - 4 and + 1

23. Simplify Rational Algebraic Expressions STEP #1 : FACTOR all expressions completely Factors of 4 that add/subtract = - 3 are - 4 and + 1 Factors of 4 that add/subtract = - 5 are - 4 and - 1

24. Simplify Rational Algebraic Expressions STEP #1 : FACTOR all expressions completely Factors of 4 that add/subtract = - 3 are - 4 and + 1 Factors of 4 that add/subtract = - 5 are - 4 and - 1 STEP # 2 : Look for COMMON FACTORS to “cancel”

25. Simplify Rational Algebraic Expressions

28. STEP #1 : FACTOR all expressions completely

29. Simplify Rational Algebraic Expressions

38. STEP #1 : FACTOR all expressions completely STEP # 2 : Look for COMMON TERMS to “cancel”