1. Chapter 6 Section 4 Addition and Subtraction of Rational Expressions

2. 1.Determine the LCD. Multiply the numerator and denominator of each fraction by any factors needed to obtain the LCD. 2.Rewrite each fraction as an equivalent fraction with the LCD. 3.Add or subtract the numerators, keep the LCD. 4.Factor and simplify the fraction when possible. Addition and Subtraction of Rational Expressions

3. Example: Addition of Rational Expressions The Commutative Property of Multiplication allows us to multiply in any order. a · b = b · a The Commutative Property of Addition allows us to add in any order. a + b = b + a Identity Property of Multiplication a · 1 = a

4. Example: Addition of Rational Expressions

5. Example: Addition of Rational Expressions

6. Example: Subtraction of Rational Expressions

7. Example: Subtraction of Rational Expressions

8. Example: Addition of Rational Expressions

9. Example: Subtraction of Rational Expressions

10. Example: Addition of Rational Expressions

11. Example: Subtraction of Rational Expressions

12. Common Errors  Treating addition and subtraction like multiplication and division. Remember you can only divide out common factors when multiplying  You must have a common denominator before you add or subtract.

13. Remember  The Commutative Property of Multiplication allows us to multiply in any order. a · b = b · a  The Commutative Property of Addition allows us to add in any order. a + b = b + a  When subtracting, you must subtract the entire numerator of the fraction that follows the minus sign by applying the distributive property. In other words, change the sign of all the second terms in the numerator when subtracting.  Simplify your final answers.

14. HOMEWORK 6.4 Page 380-381: #9, 11, 17, 25, 29, 37, 45, 49, 55, 57