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

I have

When I apply the quotient rule I have: or simplified

My question is can I take the quantity in the denominator and simplify it with the same quantities in the numerator? Since I am essentially subtracting 2 quantities of , 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:

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.