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Simplify Rational Expressions Rational Expression: a fraction whose numerators and denominators are polynomials. Examples: 3 , 2x , and 6 . x + 4 x2 – 9 x2 + 1 Domain: the set of all real numbers except those for which the denominator is zero. For example: The domain of 3 is x+4 all real numbers except -4. Simplify Rational Expression the same way that you reduce a fraction. 2x 5x Divide the numerator and denominator by “x” 2 = 5 Divide the numerator and denominator by “2” 4x 8 = 2x + 4 2 Domain:x can be any real number except a number that would make the denominator 0! Find the domain of each expression below. 3 x4 2x 2 x 9 6 x 5 x 4 x 3 x5 How do you know when your rational expression is reduced? Reduced Form: when the numerator and denominators have no common factors except for ±1. The RULE: To simplify fractions, divide out common factors. REMEMBER you can’t cancel out +(adding) and –(subtracting) For a,b,c any non-zero real numbers, ac a ac a bc b bc b Remember you can only cancel out FACTORS!!! Simplify the expression. 2 x + 4x +4 2 x -4 (x + 2)(x + 2) (x + 2)(x – 2) Factor each polynomial. What does the numerator and denominator have in common? Factor out (x + 2) The answer is: x + 2 x-2 Simplify the expression. x2 - 7x + 12 x2 +3x - 18 (x - 4)(x – 3) (x + 6)(x - 3) Factor each polynomial. What does the numerator and denominator have in common? Factor out (x – 3) The answer is: x - 4 x+6