Adding and Subtracting Rational Expressions

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

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

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

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

Let’s try one

Let’s try one

Let’s try one

Let’s try one

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

The goal is to simplify them down 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 Find LCM of denoms Treat each fraction as an individual problem. Find the LCM and add or subtract. Divide the rational expressions. Simplify

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

Let’s try one

Let’s try one