1. 5.2 Multiplying and Dividing Rational Expressions BobsMathClass.Com Copyright © 2010 All Rights Reserved. 1 Multiplying Rational Expressions Recall the General Rule for Multiplying Fractions. If a,b, and c are integers, and b and d are not equal to zero, then: Procedure: To Simplify Rational Expressions Being Multiplied 2.Multiply numerators and denominators. Write as a singlefraction. 3. Write rational expression in lowest terms 4. Write remaining factors as answer. 1. Divide out whole numbers by a common factor when possible (reduce). 2 4 35 3 rd, divide out common factors using the quotient rule for exponents. 2 nd, combine as a single fraction. Answer: 1 st, reduce whole numbers. Solution: Your Turn Problem #1

2. 5.2 Multiplying and Dividing Rational Expressions BobsMathClass.Com Copyright © 2010 All Rights Reserved. 2 Solution: Factor all numerators and denominators. Use the quotient rule for exponents to divide out like factors. Answer: Your Turn Problem #2

3. 5.2 Multiplying and Dividing Rational Expressions BobsMathClass.Com Copyright © 2010 All Rights Reserved. 3 Factor all numerators and denominators Divide out like factors. Solution: Answer: Your Turn Problem #3

4. 5.2 Multiplying and Dividing Rational Expressions BobsMathClass.Com Copyright © 2010 All Rights Reserved. 4 Dividing Algebraic Expressions Procedure: To Divide Algebraic Fractions 1. Rewrite the first fraction. 2. Write a multiplication symbol instead of the division symbol. 3. Write the reciprocal of the original second fraction. 4. Perform the multiplication as in the previous examples. Solution: 1. Recopy the first fraction. 2. Write a multiplication symbol instead of the division symbol. 3. Write the reciprocal of the original second fraction. 4. Perform the multiplication (simplify). Answer: Your Turn Problem #4

5. 5.2 Multiplying and Dividing Rational Expressions BobsMathClass.Com Copyright © 2010 All Rights Reserved. 5 Solution: 1. Rewrite the first fraction. 2. Write a multiplication symbol instead of the division symbol. 3. Write the reciprocal of the original second fraction. 4. Factor completely then divide out like factors. Answer:Your Turn Problem #5

6. 5.2 Multiplying and Dividing Rational Expressions BobsMathClass.Com Copyright © 2010 All Rights Reserved. 6 Rational Expressions That Involve Both Multiplication And Division. Procedure: To Simplify Rational Expressions That Involve Both Multiplication And Division. 1. Convert any division symbols to multiplication. 2. Invert only the fraction that originally followed the division symbols. Solution: Change the division symbol to a multiplication symbol and invert only the middle fraction. Factor all numerators and denominators. Divide out like factors. Answer: Your Turn Problem #6 The End. B.R. 12-27-06