College Algebra (6th Edition)

$\frac{2x}{x+2}$
Find the least common denominator for the terms. Then make sure to multiply the numerator by the new part of each denominator. Now combine the fractions and combine like terms. Then find the greatest common factor of the numerator that can cancel out part of the denominator. $\frac{3x}{x+2}+\frac{x}{x-2}$ $\frac{3x(x-2)}{(x+2)(x-2)}+\frac{x(x+2)}{(x+2)(x-2)}$ $\frac{3x^2-6x}{(x+2)(x-2)}+\frac{x^2+2x}{(x+2)(x-2)}$ $\frac{3x^2-6x+x^2+2x}{(x+2)(x-2)}$ $\frac{4x^2-4x}{(x+2)(x-2)}$ $\frac{2x(x-2)}{(x+2)(x-2)}$ $\frac{2x}{x+2}$