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Consider the following code:

Assuming[2 > u > 0 && 2 > x > 0, FullSimplify[Log[x]/Sqrt[4 - x^2] /. x -> 2 Sqrt[(2 - u)/(2 + u)]]]

The following output is returned:

(the TeX'd equivalent, screenshots for Mathematica output make me uneasy)

$$\frac{1}{8}\sqrt{2+\frac{4}{u}} \text{Log}\left[-4+\frac{16}{2+u} \right]$$

How can I force Together on the arguments?

i.e. I would like it to look something closer to this:

$$\frac{1}{8}\sqrt{\frac{4+2u}{u}} \text{Log}\left[\frac{8-4u}{2+u}\right]$$

FullSimplify, Together, Simplify, etc. don't change the output by any significant margin.

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    $\begingroup$ Try ExpandNumerator@*Together //@ % after evaluating your snippet. $\endgroup$ Mar 26, 2019 at 23:47
  • $\begingroup$ That worked, thanks :) +1 $\endgroup$ Mar 26, 2019 at 23:48

1 Answer 1

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Try this:

expr = Log[x]/Sqrt[4 - x^2] /. x -> 2 Sqrt[(2 - u)/(2 + u)]

(* Log[2 Sqrt[(2 - u)/(2 + u)]]/Sqrt[4 - (4 (2 - u))/(2 + u)] *)

Then:

Simplify[expr // FunctionExpand, 2 > u > 0]

yielding this:

enter image description here

Have fun!

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  • $\begingroup$ Wow.... Where has this function been for the past 4 years of my life.... $\endgroup$ Mar 27, 2019 at 9:44

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