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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.

user2355058
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  • It's worth learning how to simplify this. But if you get an exam question on the quotient rule and you're not told to simplify what you get, leave it. No chance to introduce an error, and easier for the instructor to grade. – Ethan Bolker Feb 08 '18 at 00:39

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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 $$\frac 1{x(8+x)}-\frac {\ln 8}{x^2}$$ 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.

Ross Millikan
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  • Would you please show the legal steps for producing this? – user2355058 Feb 08 '18 at 00:35
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    It is separating the fractions into a sum (or difference, not product) of fractions with denominator $x^2$ The first part just goes $\dfrac {\frac x{8+x}}{x^2}=\frac x{x^2(8+x)}=\frac1{x(8+x)}$ – Ross Millikan Feb 08 '18 at 00:57