 # 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. Makayla Reilly 2022-09-14 Answered
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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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.

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