Chapter 7: Rational Expressions Section 7.4: Adding and Subtracting Rational Expressions

Section 7.4: Adding and Subtracting Rational Expressions Goal: To add and subtract rational expressions

Section 7.4: 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 4 LCM of a2 – 6a + 9 and a2 + a – 12 6 = 2 · 3 a2 – 6a + 9 = (a – 3)2 4 = 22 a2 + a – 12 = (a – 3)(a + 4) LCM = 22 · 3 = 12 LCM = (a – 3)2(a + 4)

Section 7.4: Adding and Subtracting Rational Expressions Example 1 Find the LCM of 15a2bc3, 16b5c2, and 20a3c6

Section 7.4: 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

Section 7.4: Adding and Subtracting Rational Expressions Example 3 Simplify

Section 7.4: Adding and Subtracting Rational Expressions Example 4 Simplify

Section 7.4: Adding and Subtracting Rational Expressions Example 5 Simplify

Section 7.4: Adding and Subtracting Rational Expressions Example 6 Simplify

Section 7.4: Adding and Subtracting Rational Expressions Example 7 Simplify

Section 7.4: Adding and Subtracting Rational Expressions Example 8 Simplify

Section 7.4: Adding and Subtracting Rational Expressions Example 9 Find the slope of the line that passes through P(3/k, 1/3) and Q(1/2, 2/k)

Section 7.4: Adding and Subtracting Rational Expressions Homework: Practice Exercises: Pg. 325 #2 – 40 (even)