Simplify the complex fraction. $\frac{\left(\frac{x^2+5x-36}{x+6}\right)}{3x-12}$

A) $\frac{x+9}{3(x+6)},x\ne 4$
B) $\frac{x-9}{3(x+6)},x\ne -4$
C) $\frac{x-4}{3(x-9)},x\ne -4$
D) $\frac{x+6}{3(x-4)},x\ne 4$
E) $\frac{x+4}{3(x+9)},x\ne 4$

First, factor the numerator and denominator where possible. The numerator $\frac{x^2+5x-36}{x+6}$ simplifies to $\frac{(x+9)(x-4)}{x+6}$ after factoring $x^2+5x-36$ . The denominator $3x-12$ simplifies to $3(x-4)$ after factoring out the 3. Thus, the complex fraction simplifies to $\frac{x+9}{3(x+6)}$ , with the condition $x\ne 4$ to avoid division by zero in the original denominator.