Presentation on theme: "Adding and Subtracting Rational Expressions"— Presentation transcript:
1 Adding and Subtracting Rational Expressions Goal Determine the LCM of polynomialsGoal Add and Subtract Rational Expressions
2 What is the Least Common Multiple? Fractions require you to find the Least Common Multiple (LCM) in order to add and subtract them!Least Common Multiple (LCM) - smallest number or polynomial into which each of the numbers or polynomials will divide evenly.The Least Common Denominator is the LCM of the denominators.
3 Find the LCM of each set of Polynomials 1) 12y2, 6x2LCM = 12x2y22) 16ab3, 5a2b2, 20acLCM = 80a2b3c3) x2 – 2x, x2 - 4LCM = x(x + 2)(x – 2)4) x2 – x – 20, x2 + 6x + 8LCM = (x + 4) (x – 5) (x + 2)
4 Adding Fractions - A Review LCD is 12.Find equivalentfractions using theLCD.Collect the numerators,keeping the LCD.
5 Remember: When adding or subtracting fractions, you need a common denominator! When Multiplying or Dividing Fractions, you don’t need a common Denominator
6 Steps for Adding and Subtracting Rational Expressions: 1. FactorIf possible, Cancel common factors directly over each other.Get a common denominatorList out factorsMultiply by 1’sAdd the top (combine like terms)Re-factor and simplify if possible4. Reduce, if possible.5. Leave the denominators in factored form.
7 Addition and Subtraction Is the denominator the same?? Example: SimplifyFind the LCD: 6xNow, rewrite the expression using the LCD of 6xSimplify...Add the fractions...= 196x