Adding and Subtracting Rational Expressions Algebra 2 Section 9-2 Adding and Subtracting Rational Expressions

To find ⅜-⅓, you must find the LCD (Least Common Denominator) To find ⅜-⅓, you must find the LCD (Least Common Denominator). The LCD is the LCM (Least Common Multiple) of the denominators, 8 and 3. 2 LCM of a – 6a + 9 and a + a – 12 a – 6a + 9 = a + a – 12 = LCM = LCM of 3 and 8 3 = 8 = LCM = 2 3 2 2 3 (a – 3) 2 x 2 x 2 = 2 2 (a – 3)(a + 4) 3 x 2 x 2 x 2 =24 2 (a – 3) ( a + 4)

Use each factor the greatest number of times it appears as a factor. 2 5 3 2 3 Find the LCM of 18r s , 24r st , and 15s t 2 5 2 2 5 18r s = 24r st = 15s t = LCM = = 360r s t 2 x 3 x r x s 3 2 3 3 2 2 x 3 x r x s x t Factor each monomial. 3 3 3 x 5 x s x t Use each factor the greatest number of times it appears as a factor. 3 2 3 5 2 2 x 3 x 5 x r x s t 3 5 2

Find the LCM of p + 5p + 6p and p + 6p + 9 3 2 2 Find the LCM of p + 5p + 6p and p + 6p + 9 3 2 p + 5p + 6p = p( p + 2 )( p + 3 ) 2 2 p + 6p + 9 = ( p + 3 ) 2 LCM = p( p + 2 )( p + 3 )

As with fractions, to add or subtract rational expressions, the terms must have common denominators. LCD: 50

7x y Simplify + LCD = 90xy² 15y² 18xy 7x y 7x(6x) y(5y) + = + 15y² 18xy 15y²(6x) 18xy(5y) 42x² 5y² = + 90xy² 90xy² 42x² + 5y² = x≠0, y≠0 90xy²

Simplify LCD = x² - 1 or (x – 1)(x + 1) Create a common denominator. Cannot be reduced any farther.

1 + Simplify 1 1 - x y LCD for numerator: LCD for denominator: xy 1 x 1 + x 1(y) 1(x) y x - - x(y) y(x) xy xy = 1(x) 1 x 1 + + 1(x) x x x

The fraction bar represents division. y - x y - x x + 1 Multiply by the reciprocal. xy ÷ xy x x + 1 y - x x • x xy x + 1 The fraction bar represents division. y - x x 1 • xy x + 1 1(y – x) y(x + 1) y - x xy + y

Homework Page 482 #23-49 odd