9.5 – Adding and Subtracting Rational Expressions

In order to add or subtract fractions we need a common denominator We want the Lowest Common Denominator (LCD) before we add or subtract LCD: 15LCD: 36

ADDING and SUBTRACTING RATIONALS - Finding LCM 10x², 35x²  _______________________ 4x³, 5x²y  _______________________ x-y, x²-y²  _______________________ x²-5x+4, x – 2  ___________________ 70x² 20x³y (x-y)(x+y) (x-4)(x-1)(x-2)

ADDING and SUBTRACTING Adding ADD/SUBTRACT Rules 1)Factor denominators 2)Find LCM 3)Multiply each term to get denominator = LCM 4)+/- and combine like terms 5)Simplify more if possible

ADDING and SUBTRACTING Subtracting Factor denominators Multiply terms to get LCMs on bottom Simplify Combine like termsFactor top Simplify

ADDING and SUBTRACTING A Toughie FACTOR FACTOR -OUT CONVERT SIMPLIFY COMBINE SIMPLIFY

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COMPLEX FRACTIONS What are complex fractions? Complex fractions are giant expressions where there are fractions within fractions. The goal is to simplify them down to normal fractions.

EX – simplify SIMPLIFYING COMPLEX FRACTIONS STEPS 1)Find LCM of denoms 2)Treat each fraction as an individual problem. Find the LCM and add or subtract. 3)Divide the rational expressions. 4)Simplify

EX - simplify FACTOR OUT -1 MULT TOP/BOT by LCM DISTRIBUTE LCM SIMPLIFY DIVIDE THE RATIONALS

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