1. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Hawkes Learning Systems: Developmental Mathematics Section 13.2: Addition and Subtraction with Rational Expressions

2. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Addition with Rational Expressions For polynomials P, Q, and R, with Q ≠ 0,

3. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Adding Rational Expressions with a Common Denominator Find each sum and reduce if possible. (Note the importance of the factoring techniques we studied in Chapter 12.)

4. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Adding Rational Expressions with a Common Denominator

5. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Addition with Rational Expressions To Find the LCM for a Set of Polynomials 1.Completely factor each polynomial (including prime factors for numerical factors). 2.Form the product of all factors that appear, using each factor the most number of times it appears in any one polynomial.

6. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Addition with Rational Expressions Procedure for Adding Rational Expressions with Different Denominators 1.Find the LCD (the LCM of the denominators). 2.Rewrite each fraction in an equivalent form with the LCD as the denominator. 3.Add the numerators and keep the common denominator. 4.Reduce if possible.

7. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Adding Rational Expressions with Different Denominators Find each sum and reduce if possible. Assume that no denominator has a value of 0.

8. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Adding Rational Expressions with Different Denominators

9. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Addition with Rational Expressions Perform the indicated addition and reduce if possible. Assume that no denominator is 0.

10. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Addition with Rational Expressions Important Note about the Form of Answers Denominators can be left in factored form as a convenience for possibly reducing or adding to some other expression later. You may choose to multiply out these factors. Either form is correct. For consistency, denominators are left in factored form in the answers in the back of the text.

11. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Subtraction with Rational Expressions Placement of Negative Signs If P and Q are polynomials and Q ≠ 0, then Subtraction with Rational Expressions For polynomials P, Q, and R, with Q ≠ 0,

12. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Subtracting Rational Expressions with a Common Denominator Find each difference and reduce if possible. Assume that no denominator has a value of 0.

13. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Subtracting Rational Expressions with a Common Denominator

14. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Subtraction with Rational Expressions

15. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Subtracting Rational Expressions with Different Denominators

16. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Subtracting Rational Expressions with Different Denominators

17. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Subtracting Rational Expressions with Different Denominators

18. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Addition with Rational Expressions