Lesson 9.2 Adding & Subtracting Fractions Finding the LCM [1] Factor the polynomials [2] Use each factor the greatest it appears as a factor Example 1 LCM of Monomials a) 12x2y5, 24x3y2z5, and 48x3z 48x3y5z5 b) 30ab3, 5a2b2, 20ac 60a2b3c

Example 2 LCM of Polynomials a) p3 + 5p2 + 6p and p2 + 6p + 9 p(p + 2)(p + 3) (p + 3)(p + 3) = (p + 3)2 LCM: p(p + 2)(p + 3)2 b) x2 – 2x and x2 – 4 x(x – 2) (x + 2)(x – 2) LCM: x(x + 2)(x – 2)

Adding Rational Expressions (Fractions) [1] Factor denominators [2] Determine the LCD (LCM of denominators) [3] Multiply Numerators to balance LCD Example 3 Monomial Denominators a) (x) (4) b) x2 + 8

Example 3 Continued (3x2) (2) c) d) 4 – 3x3 14x2 + 15y2 6x2y 30xy2

Examples 4: Polynomial Denominators = (x – 5)(x + 4) (x – 5)(x + 4) 2x + 10 (x + 5) b) – x – 10 = (x + 5)2 (x + 5)(x + 5) (x + 5)2