Simplify Rational Expressions

**Simplify Rational Expressions**

**Goal: Simplify Rational Expressions**

**Example**

Simplify:

The common factors in the numerator and denominator cancel out because any expression divided by itself is 1; therefore,Factor the numerator: 3x+ 6 = 3(x+ 2)

Factor the denominator: 2x+ 4 = 2(x+ 2)

Rewrite the expression in terms of the factors:

**Example**

Simplify:

Factor the numerator:x- 24 = 4(x6)

Factor the denominator:x^{2}- 9x+ 18 = (x6)(x3)

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