I have the result of a quotient rule:
$$ \frac{\frac{x}{8+x}-ln8}{x^2} $$
Should I just leave it? Would it be appropriate to separate the fraction into a product of fractions with denominator $x^2$, simplify the left side, and give the result as a product of two fractions?
Any soln using addition or subtraction of fractions is unacceptable and messier than just leaving as is.
Simplification is often in the eye of the beholder. I think most people dislike compound fractions, so I would take this to $$\frac 1{x(8+x)}-\frac {\ln 8}{x^2}$$ Whether you expand the first denominator is a matter of taste. You might also put the two fractions over a common denominator. Take your pick.