Combine and simplify. $\frac{x}{x+4}-\frac{3}{x-7}$

A) $\frac{x^2-10x-12}{(x+4)(x-7)}$
B) $\frac{x(x-11)}{(x+3)}$
C) $\frac{x(x-7)}{(x+7)(x-4)}$
D) $\frac{x^2-7}{(x+3)(x-4)}$
E) $\frac{x-3}{(x+4)(x-7)}$

To combine and simplify the given expression, we need to find a common denominator for the two fractions. The common denominator will be $(x+4)(x-7)$, so we need to rewrite the given fractions with this denominator. We can do this by multiplying the numerator and denominator of the first fraction by $(x-7)$ and the numerator and denominator of the second fraction by $(x+4)$. This gives us: $$\frac{x(x-7)}{(x+4)(x-7)}-\frac{3(x+4)}{(x+4)(x-7)}$$ Simplifying this expression gives: $$\frac{x(x-7)-3(x+4)}{(x+4)(x-7)}$$ Multiplying out the brackets on the numerator gives: $$\frac{x^2-7x-3x-12}{(x+4)(x-7)}$$ Combining like terms on the numerator gives: $$\frac{x^2-10x-12}{(x+4)(x-7)}$$ Therefore, the answer is A.