This is more of an algebra question than calculus, but it involves derivatives so I thought I'd post it here.

I have $\displaystyle f(x) = \frac{5x}{(3-5x)^2} $

When I apply the quotient rule I have: $\displaystyle f'(x) = \frac{5x[2(3-5x)]*(-5)-5(3-5x)^2}{[(3-5x)^2]^2}$ or $\displaystyle f'(x) = \frac{-50x(3-5x)-5(3-5x)^2}{(3-5x)^4}$ simplified

My question is can I take the quantity $\displaystyle (3-5x)^4 $ in the denominator and simplify it with the same quantities in the numerator? Since I am essentially subtracting 2 quantities of $\displaystyle (3-5x) $ , would I be cancelling out the term to the far right completely, and leaving the term on the far left with a quantity of -1? Thus that leaves the denominator with the 3 quantities? I remember my professor saying something about all derivatives of rational functions will increment by 1 in the denominator.

To get: $\displaystyle f'(x) = \frac{-50x-5}{(3-5x)^3} $

This is just something I never fully understood with quantities learning algebra, but now I kind of have to face it with these kinds of calculus problems.