Answer :
ANSWER
[tex]\begin{gathered} -\frac{4(x+6)}{(x-5)(x+5)} \\ x\ne\pm5,\pm6,0 \end{gathered}[/tex]EXPLANATION
We want to simplify the expression:
[tex]-\frac{4x}{x^2-25}\div\frac{(x^2-6x)}{x^2-36}[/tex]To do this, first change the sign to a multiplication sign and flip the fraction on the right:
[tex]-\frac{4x}{x^2-25}\cdot\frac{x^2-36}{(x^2-6x)}[/tex]Now, simplify the expression by applying the difference of two squares and factorization:
[tex]\begin{gathered} -\frac{4x}{(x-5)(x+5)}\cdot\frac{(x-6)(x+6)}{x(x-6)} \\ \Rightarrow-\frac{4}{(x-5)(x+5)}\cdot\frac{(x+6)}{1} \\ \Rightarrow-\frac{4(x+6)}{(x-5)(x+5)} \end{gathered}[/tex]The expression will be invalid when x is:
[tex]\pm5,\pm6,0[/tex]Therefore, the answer is option C.