2 Rational Expression: a fraction whose numerators and denominators are polynomials. Examples: , 2x , and x x2 – x2 + 1
3 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.
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=
5 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.
6 How do you know when your rational expression is reduced? Reduced Form: when the numerator and denominators have no common factors except for ±1.
7 The RULE: To simplify fractions, divide out common factors. REMEMBER you can’t cancel out +(adding) and –(subtracting)
8 Remember you can only cancel out FACTORS!!! For a,b,c any non-zero real numbers,Remember you can only cancel out FACTORS!!!
9 Simplify the expression. Factor each polynomial. x2 + 4x +4Factor 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
10 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