Mastering Addition and Subtraction of Rational Expressions Made Easy

1. 9.5 – Adding and Subtracting Rational Expressions

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

3. ADDING and SUBTRACTINGRATIONALS - 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)

4. ADDING and SUBTRACTINGAdding ADD/SUBTRACT Rules Factor denominators Find LCM Multiply each term to get denominator = LCM +/- and combine like terms Simplify more if possible

5. ADDING and SUBTRACTINGSubtracting Factor denominators Multiply terms to get LCMs on bottom Simplify Simplify Combine like terms Factor top

6. ADDING and SUBTRACTINGA Toughie FACTOR FACTOR -OUT CONVERT SIMPLIFY COMBINE SIMPLIFY

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11. 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.

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

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

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