1.  Chapter 8 – Rational Expressions and Equations 8.2 – Adding and Subtracting Rational Expressions

2.  Today we will be learning how to:  Determine the LCM of polynomials  Add and subtract rational expressions

3. 8.2 – Adding and Subtracting Rational Expressions  To find 5/6 – 1/4, you must first find the least common denominator (LCD). The LCD is the least common multiple (LCM) of the denominators.  To find the LCM of two or more numbers or polynomials, factor each number or polynomial. The LCM contains each factor the greatest number of times it appears as a factor  LCM of 6 and 4LCM of a 2 – 6a + 9 and a 2 + a – 12  6 = 2 · 3a 2 – 6a + 9 = (a – 3) 2  4 = 2 2 a 2 + a – 12 = (a – 3)(a + 4)  LCM = 2 2 · 3 = 12LCM = (a – 3) 2 (a + 4)

4. 8.2 – Adding and Subtracting Rational Expressions  Example 1  Find the LCM of 15a 2 bc 3, 16b 5 c 2, and 20a 3 c 6

5. 8.2 – Adding and Subtracting Rational Expressions Add and Subtract Rational Expressions As with fractions, to add or subtract rational expression, you must have common denominators  Specific Case  2/3 + 3/5  General case  a/c + b/d

6. 8.2 – Adding and Subtracting Rational Expressions  Example 3  Simplify

7. 8.2 – Adding and Subtracting Rational Expressions  Example 4  Simplify

8. 8.2 – Adding and Subtracting Rational Expressions  Example 5  Simplify

9. 8.2 – Adding and Subtracting Rational Expressions  Example 6  Find the slope of the line that passes through P(3/k, 1/3) and Q(1/2, 2/k)

10. 8.2 – Adding and Subtracting Rational Expressions HOMEWORK Page 454 #18 – 32 (even), 35