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. Factor, if necessary.2. Cancel common factors, if possible.3. Look at the denominator.4. Reduce, if possible.5. Leave the denominators in factored form.If the denominators are the same,add or subtract the numerators and place the result over the common denominator.If the denominators are different,find the LCD. Change the expressions according to the LCD and add or subtract numerators. Place the result over the common denominator.
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
8 Simplify: 6(3mn2) + 8(5n) - 7(15m) Multiply by 5n LCD = 15m2n2 m ≠ 0 Example 16(3mn2)+ 8(5n)- 7(15m)Multiply by5nLCD = 15m2n2m ≠ 0n ≠ 0Multiply by3mn2Multiply by15m