Simplifying Rational Expressions Math Example 2

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

Example 2

easy
Simplify 4x22x\frac{4x^2}{2x}.

Solution

  1. 1
    Step 1: Factor: 4x22x=2โ‹…2โ‹…xโ‹…x2โ‹…x\frac{4x^2}{2x} = \frac{2 \cdot 2 \cdot x \cdot x}{2 \cdot x}.
  2. 2
    Step 2: Cancel common factors 22 and xx: 2x2x.
  3. 3
    Step 3: Domain restriction: xโ‰ 0x \neq 0.

Answer

2x2x, xโ‰ 0x \neq 0
The simplest rational expressions simplify by dividing coefficients and subtracting exponents. Even simple cases require noting where the original denominator equals zero.

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 3 easy

Simplify [formula].

Example 4 hard

Simplify [formula].

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