Example

Rewriting 2x2x12\frac{2}{x^2-x-12} and 1x216\frac{1}{x^2-16} with LCD (x+3)(x4)(x+4)(x+3)(x-4)(x+4)

Rewrite the rational expressions 2x2x12\frac{2}{x^2-x-12} and 1x216\frac{1}{x^2-16} as equivalent expressions with the lowest common denominator (x+3)(x4)(x+4)(x + 3)(x - 4)(x + 4).

Step 1 — Multiply each expression by its missing factor. The first denominator is missing (x+4)(x + 4), so multiply the numerator and denominator by (x+4)(x + 4): 2(x+4)(x4)(x+3)(x+4)\frac{2(x + 4)}{(x - 4)(x + 3)(x + 4)} The second denominator is missing (x+3)(x + 3), so multiply the numerator and denominator by (x+3)(x + 3): 1(x+3)(x4)(x+4)(x+3)\frac{1(x + 3)}{(x - 4)(x + 4)(x + 3)}

Step 2 — Simplify the numerators. Distributing the numerators yields the equivalent expressions: 2x+8(x+3)(x4)(x+4)\frac{2x + 8}{(x + 3)(x - 4)(x + 4)} and x+3(x+3)(x4)(x+4)\frac{x + 3}{(x + 3)(x - 4)(x + 4)}

0

1

Updated 2026-04-30

Contributors are:

Who are from:

Tags

OpenStax

Intermediate Algebra @ OpenStax

Ch.7 Rational Expressions and Functions - Intermediate Algebra @ OpenStax

Algebra

Related