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Warm – Up2/12/07 Simplify the following 3 1 1) 15 5 2 3x 2) 15 x 2 x 5 2 3 x y 3) 3 15 xy x 5y Agenda Notes on Rational Expressions Questions Homework Assignment Tues: More Simplifying Rational Expressions WEB: Multiply & Divide Rational Expressions Thur: Review Rational Expressions Friday 2/16 Quiz: 11.4 – 11.5 Simplifying Rational Expressions Let’s start with what’s a rational number – a number that can be written as the quotient of two integers. HUH? What does that mean? Here are a few examples of Rational Numbers: ½, ⅓, ¼, ¾ You mean they’re just fractions? YEP – that’s it - Rationals are fractions!! Sooooo What does that have to do with RATIONAL EXPRESSIONS? Remember what an expression looks like? 3 2 Here’s one: 3 x 9 x x 7 So if Rationals look like fractions and Expressions have terms added and subtracted, then a Rational Expression is…. …..a Fraction with terms that have variables and numbers Here are a few examples: 7 x3 5x 2 x 16 2x 1 2 x 1 Let’s simplify a few… Recall how to simplify the fractions: Use the same steps for Rational Expressions 12 12 1 1 36 12 3 3 This x is a term NOT a Only cancel Factor common FACTORS 5 x 5 5( x 1) ( x 1) 5x 5x x Only cancel common FACTORS Simplify 2 2 x x 2x 2x 2 x 5 x x( x 5) x 5 Only cancel common FACTORS Let’s talk about plain ole fractions again…. What happens if there is a zero in the denominator of a fraction? 7 0 We say this is ‘undefined’ Likewise Rational Expressions with zero in the denominator is also ‘undefined’ We’ll always determine what would make the denominator zero and exclude those values for the variable. 7 x3 5x 2 x 16 2x 1 2 x 1 Undefined Expressions One way to determine what will make the denominator zero is to set it equal to zero. 2x 1 2 x 1 Set the denominator equal to zero and solve – this is what we do NOT want!!! x 1 0 2 x 1 x 1 2 So x can be anything except +1 and -1!!! Let’s look at the we just worked. For what value of the variable is the expression undefined? 15 x 5 5(3x 1) (3x 1) 5x 5x x 2 2x x 2x 2x 2 x 5 x x( x 5) x 5 x=0 would make the expression undefined x=-5 would make the expression undefined Homework p.667: 1-5 all; 9-18 all