Multiply and simplify. $\frac{(4x-9)(x+9)}{x^6}\cdot \frac{x}{9-4x}$

A) $\frac{324}{9-4x},x\ne \frac{4}{9}$
B) $\frac{x-9}{x^6},x\ne -9$
C) $-\frac{x+9}{x^5},x\ne \frac{9}{4}$
D) $-\frac{x+9}{x^7},x\ne -\frac{4}{9}$
E) $\frac{(4x-9)(x+9)}{36},x\ne -\frac{9}{4}$

First, we need to simplify the expression:
$$\frac{(4x-9)(x+9)}{x^6}\cdot \frac{x}{9-4x}=\frac{(4x-9)(x+9)x}{x^6(9-4x)}=\frac{(4x-9)(x+9)x}{x^5(x-9)}=\frac{(4x-9)(x+9)}{x^4(x-9)}.$$
Next, we need to simplify the expression further by factoring the numerator:
$$\frac{(4x-9)(x+9)}{x^4(x-9)}=\frac{(4x-9)\cdot 3^2}{x^4(x-9)}=\frac{3^2(4x-9)}{x^4(9-4x)}.$$
The final simplified expression has the same denominator as the original expression, but the numerator is different. Therefore, option C, $-\frac{x+9}{x^5},$ cannot be correct. The correct answer is option A, $\frac{324}{9-4x},$ since it has the same denominator and simplified numerator. However, we need to add the restriction $x\neq\frac{9}{4}$ due to the denominator of the second fraction in the original expression.