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**Simplify Rational Expressions**

11.5 Simplify Rational Expressions

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**Rational Expression: a fraction whose numerators and denominators are polynomials.**

Examples: , 2x , and x x2 – x2 + 1

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**Domain: the set of all real numbers except those for which the denominator is zero.**

For example: The domain of is x all real numbers except -4.

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**Simplify Rational Expression the same way that you reduce a fraction.**

Divide the numerator and denominator by “x” 2 5 = Divide the numerator and denominator by “2” 2x + 4 =

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**Find the domain of each expression below.**

Domain:x can be any real number except a number that would make the denominator 0! Find the domain of each expression below.

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**How do you know when your rational expression is reduced?**

Reduced Form: when the numerator and denominators have no common factors except for ±1.

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**The RULE: To simplify fractions, divide out common factors.**

REMEMBER you can’t cancel out +(adding) and –(subtracting)

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**Remember you can only cancel out FACTORS!!!**

For a,b,c any non-zero real numbers, Remember you can only cancel out FACTORS!!!

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**Simplify the expression. Factor each polynomial.**

x2 + 4x +4 Factor each polynomial. x2 - 4 (x + 2)(x + 2) (x + 2)(x – 2) What does the numerator and denominator have in common? Factor out (x + 2) The answer is: x x - 2

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**Simplify the expression.**

Factor each polynomial. x2 - 7x + 12 x2 +3x - 18 (x - 4)(x – 3) (x + 6)(x - 3) What does the numerator and denominator have in common? Factor out (x – 3) The answer is: x x + 6

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