1. MTH095 Intermediate Algebra Chapter 7 – Rational Expressions Section 7.3 – Addition and Subtraction of Rational Expressions Copyright © 2010 by Ron Wallace, all rights reserved.

2. Review … Adding Fractions w/ Common (i.e. same) Denominators Why? It’s just the distributive property!

3. Review … Adding Fractions w/ Common (i.e. same) Denominators Subtracting Fractions w/ Common (i.e. same) Denominators Don’t forget to simplify!

4. Review … Adding Fractions wo/ Common (i.e. different) Denominators Subtracting Fractions wo/ Common (i.e. different) Denominators Don’t forget to simplify!

5. Least Common Multiple (LCM) AKA: Least Common Denominator (LCD) LCM = Smallest expression that two other expressions divide into evenly. With numbers … 1.Factor w/ Primes 2.LCM = product of each factor raised to the highest power found in the factorization of the two numbers.

6. Least Common Multiple (LCM) AKA: Least Common Denominator (LCD) Examples with Numbers: ◦ Find the LCM of 20 & 70 ◦ Find the LCM of 90 & 220

7. Least Common Multiple (LCM) AKA: Least Common Denominator (LCD) LCM = Smallest expression that two other expressions divide into evenly. With polynomials… 1.Factor 2.LCM = product of each factor raised to the highest power found in the factorization of the two polynomials.

8. Least Common Multiple (LCM) AKA: Least Common Denominator (LCD) Examples with Polynomials: ◦ Find the LCM of x 2 – 9 & 4x – 12 ◦ Find the LCM of x 3 + 2x 2 – 3x & x 4 – x 2

9. “Un-Reducing” a Fraction Change the following fraction into an equivalent fraction with a denominator of 30. a.Factor both old & new denominators. b.Divide the new denominator by the old denominator (i.e. cancel out factors). c.Multiply the old numerator by the result of the above division. Our book calls this “building up” a fraction.

10. “Un-Reducing” a Rational Expression Change the following rational expression into an equivalent rational expression with a denominator of x(x+2)(x–2 )2 (x+3). a.Factor both old & new denominators. b.Divide the new denominator by the old denominator (i.e. cancel out factors). c.Multiply the old numerator by the result of the above division. Our book calls this “building up” a fraction.

11. Adding Rational Expressions w/ Common (i.e. same) Denominators That is … 1.Add numerators together. 2.Keep the same denominator. 3.Simplify (factor & cancel common factors) NOTE: Subtraction is the same, except that you subtract instead of add!

12. Adding Rational Expressions w/ Common (i.e. same) Denominators ----- Examples -----

13. Adding Rational Expressions wo/ Common (i.e. different) Denominators The Process (just like with numbers) … 1.Find the common denominator (LCD). This will be the denominator of the sum. 2.Un-Reduce both rational expressions so they end up with the same denominators (i.e. the LCD). 3.Add the fractions (they now have common denominators). 4.Simplify (factor & cancel common factors) NOTE: Subtraction is the same, except that you subtract instead of add!

14. Adding Rational Expressions wo/ Common (i.e. different) Denominators ----- Examples ----- 1 of 5 The Process… 1.Find the common denominator. 2.Un-Reduce both rational expressions. 3.Add the fractions. 4.Simplify.

15. Adding Rational Expressions wo/ Common (i.e. different) Denominators ----- Examples ----- 2 of 5 The Process… 1.Find the common denominator. 2.Un-Reduce both rational expressions. 3.Add the fractions. 4.Simplify.

16. Adding Rational Expressions wo/ Common (i.e. different) Denominators ----- Examples ----- 3 of 5 The Process… 1.Find the common denominator. 2.Un-Reduce both rational expressions. 3.Add the fractions. 4.Simplify.

17. Adding Rational Expressions wo/ Common (i.e. different) Denominators ----- Examples ----- 4 of 5 The Process… 1.Find the common denominator. 2.Un-Reduce both rational expressions. 3.Add the fractions. 4.Simplify.

18. Adding Rational Expressions wo/ Common (i.e. different) Denominators ----- Examples ----- 5 of 5 The Process… 1.Find the common denominator. 2.Un-Reduce both rational expressions. 3.Add the fractions. 4.Simplify.