# Simplify fraction in numerator when fraction is part of sum I have the result of a quotient rule: ((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.

Simplify fraction in numerator when fraction is part of sum
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.
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Dante Patton
Simplification is often in the eye of the beholder. I think most people dislike compound fractions, so I would take this to
$\frac{1}{x\left(8+x\right)}-\frac{\mathrm{ln}8}{{x}^{2}}$
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.