Simplify Rational Expressions 11.5 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. Divide the numerator and denominator by “x” 2 5 = Divide the numerator and denominator by “2” 2x + 4 =

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.

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)

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

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 + 2 x - 2

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 - 4 x + 6