GENERAL RULES: Add and Subtract Fractions Finding the LCM “Common Denominator” [1] Factor the polynomials [2] Use the greatest power of each different factor Example 1LCM of Monomials a) 12x 2 y 5, 24x 3 y 2 z 5, and 48x 3 z b) 30ab 3, 5a 2 b 2, 20ac

Example 2LCM of Polynomials a)p 3 + 5p 2 + 6p and p 2 + 6p + 9 b)x 2 – 2x and x 2 – 4 c)y 3 – 6y 2 + 8y and 3y 2 – 12y + 12

Add and Subtract Rational Expressions (Fractions) [1] FACTOR all denominators [2] Find COMMON Denominator (LCM of denominators) [3] Each Numerator, multiply by necessary factors to create common denominator. Be careful to distribute, FOIL, and laws of exponents. [4] Add or Subtract Numerators to create one fraction with common denominator [5] SIMPLIFY, as needed

c) d) Example 3Monomial Denominators b) a)

g) h) Example 3: Continued f) e)

Examples 4: Polynomial Denominators a) b) c)

Examples 4: Continued d) e) f)g)

Examples 5: Simplify Each Expression b) a) d)e) c)