Simplifying Rational Expressions Math Example 3

Follow the full solution, then compare it with the other examples linked below.

Example 3

easy
Simplify x2โˆ’4x+2\frac{x^2 - 4}{x + 2}.

Solution

  1. 1
    Factor: (x+2)(xโˆ’2)x+2=xโˆ’2\frac{(x+2)(x-2)}{x+2} = x - 2, xโ‰ โˆ’2x \neq -2.
  2. 2
    Check: At x=3x = 3: 9โˆ’45=1\frac{9-4}{5} = 1 and 3โˆ’2=13-2 = 1 โœ“

Answer

xโˆ’2x - 2, xโ‰ โˆ’2x \neq -2
Recognizing the numerator as a difference of squares is key. After factoring, the (x+2)(x+2) cancels with the denominator.

About Simplifying Rational Expressions

Simplifying a rational expression p(x)q(x)\frac{p(x)}{q(x)} by factoring both the numerator and denominator, then canceling common factors. The domain must exclude values that make any original denominator zero.

Learn more about Simplifying Rational Expressions โ†’

More Simplifying Rational Expressions Examples

Example 1 medium

Simplify [formula].

Example 2 easy

Simplify [formula].

Example 4 hard

Simplify [formula].

โ† All Simplifying Rational Expressions Examples Simplifying Rational Expressions Concept