To simplify the expression, we need to find a common denominator for the two fractions.

The common denominator for [tex]x-6[/tex] and [tex]36-x^{2}[/tex] is tex(36-x^{2})[/tex].

Now, we rewrite the expression with the common denominator:

[tex]\frac{2x(36-x^{2})}{(x-6)(36-x^{2})} - \frac{(5x-2)(x-6)}{(x-6)(36-x^{2})}[/tex]

Now, we simplify the expression further:

[tex]\frac{72x - 2x^{3} - 5x^{2} + 30x}{(x-6)(36-x^{2})}[/tex]

[tex]=\frac{-2x^{3}-5x^{2}+102x}{(x-6)(36-x^{2})}[/tex]