Subtract. (2x)/(x+2)-(4x)/(x-4) Simplify your answer as much as possible. square

To subtract the given fractions, we need to find a common denominator. The common denominator for $\frac{2x}{x+2}$ and $\frac{4x}{x-4}$ is $(x+2)(x-4)$.<br /><br />Rewriting the fractions with the common denominator, we have:<br />$\frac{2x(x-4)}{(x+2)(x-4)} - \frac{4x(x+2)}{(x+2)(x-4)}$<br /><br />Combining the fractions, we get:<br />$\frac{2x(x-4) - 4x(x+2)}{(x+2)(x-4)}$<br /><br />Simplifying the numerator, we have:<br />$\frac{2x^2 - 8x - 4x^2 - 8x}{(x+2)(x-4)}$<br /><br />Combining like terms, we get:<br />$\frac{-2x^2 - 16x}{(x+2)(x-4)}$<br /><br />Factoring out $-2x$ from the numerator, we have:<br />$\frac{-2x(x + 8)}{(x+2)(x-4)}$<br /><br />Therefore, the simplified answer is:<br />$\boxed{\frac{-2x(x + 8)}{(x+2)(x-4)}}$