Simplify Rational Expressions

Goal: Simplify Rational Expressions

Example

Simplify:
Factor the numerator: 3x + 6 = 3(x + 2)

Factor the denominator: 2x + 4 = 2(x + 2) 
Rewrite the expression in terms of the factors:
The common factors in the numerator and denominator cancel out because any expression divided by itself is 1; therefore,
Example

Simplify:
Factor the numerator: x - 24 = 4(x 6)

Factor the denominator: x2 - 9x + 18 = (x 6)(x 3)
Rewrite the expression in terms of the factors: =
Identify the common factors in the numerator and the denominator. These two factors cancel out because any expression divided by itself is 1.
=


It is important to know that rational expressions have restrictions on the variables so that denominators cannot equal zero. Thus, in the previous examples

; x 2 and ;x 3 or 6