Display of nested fractions as products of fractions

Question

How do I get Mathematica to avoid displaying nested fractions in outputs, and instead automatically display them as parenthesized, factored-out terms?

For example, I would like

(A/(B + C) + D)/F

to be displayed as $\frac{1}{F} \left(\frac{A}{B+C}+D\right)$ instead of $\frac{\left(\frac{A}{B+C}+D\right)}{F}$.

If possible, I would like to do this in a somewhat automated manner, without having to manually Inactivate multiplications, for instance.

It would be great if the solution could work for "higher-order" nested fractions too. For instance:

((A/(B + C) + D)/F + G)/H

could be displayed as $\frac{1}{H}\left(\frac{1}{F}\left(\frac{A}{B+C}+D\right)+G\right)$

Consider an actual example of expression that I have in my code:

L^2 + (-4 + (6 L)/J + (L^2 (7 - 2 \[Nu]))/J^2 + (L^4 (-9 + \[Nu]))/   J^4 + \[Nu])/c^2 + ((L (77/2 - 11 \[Nu]))/J^3 + (4 + \[Nu]/4)/   L^2 + (3 L^3 (-9 + \[Nu]))/J^5 + (-(39/2) + 6 \[Nu])/(J L) + (   L^4 (-6920 + 2580 \[Nu] - 179 \[Nu]^2))/(32 J^6) + (   168 + 12 \[Nu] + \[Nu]^2)/(32 J^2) + (   7 L^6 (360 - 96 \[Nu] + 7 \[Nu]^2))/(16 J^8) + (   L^2 (294 - 149 \[Nu] + 10 \[Nu]^2))/(4 J^4))/c^4

I would like to ideally have an output similar to:

$ L^2 + \frac{1}{c^2}\left(\frac{L^4 (\nu -9)}{J^4}+\frac{L^2 (7-2 \nu )}{J^2}+\frac{6 L}{J}+\nu -4\right) +\frac{1}{c^4}\left(\frac{7 L^6 \left(7 \nu ^2-96 \nu +360\right)}{16 J^8}+\frac{L^4 \left(-179 \nu ^2+2580 \nu -6920\right)}{32 J^6}+\frac{3 L^3 (\nu -9)}{J^5}+\frac{L^2 \left(10 \nu ^2-149 \nu +294\right)}{4 J^4}+\frac{L \left(77-22\nu \right)}{2 J^3}+\frac{\nu ^2+12 \nu +168}{32 J^2}+\frac{12 \nu - 39}{2 J L}+\frac{\nu + 16}{4 L^2} \right) $

Answer 1

Since this is for display only, how about

ClearAll["Global`*"]
makeNice[e_] :=  If[Denominator[e] =!= 1, 1/Denominator[e]·Numerator[e], e]

And now you can use it as follows

makeNice[(a/(b + c) + d)/f]

makeNice[(1 + x)/(x*Sin[x])/4]

Tested only on small examples. Feel free to test it more and see if you find any bugs and will try to fix. This can be made more robust by adding more checks on the input ofcourse.

But you can't use the output since it uses center dot for multiplications. You could always replace the center dot with the real * to use it.

This works only on one term. To make it work on sum of terms, it is easy to do that. For example, given

e = (a/(b + c) + d)/f + x + (a/(b + c) + d)/g

Then you can do

 Map[makeNice, e]

Answer 2

Although @Nasser has provided a great straightforward answer for simple cases, more complex nested fractions might require a pattern-matching solution. The following should work for a great variety of cases.

First, we define a pattern-testing function to determine whether an expression has a non-trivial denominator in any subexpression. This can be done with FreeQ:

denominatorFreeQ[expr_] := FreeQ[expr, x_ /; !SameQ[Denominator[x], 1]];

As a test, we can apply denominatorFreeQ to a few sample cases:

denominatorFreeQ /@ 
    {a, a/x, (a + b)/(x + y), a (b + c), a (b + c/x), a b (c + (d + e/2))}

The main function can now check an expression for subexpressions whose numerators aren't denominator-free, and inactivate the Times.

formatNestedTimes = ReplaceRepeated[
              x_ /; And[!denominatorFreeQ[Numerator[x]],!SameQ[Denominator[x], 1]]
              :> Inactive[Times][1/Denominator[x], Numerator[x]]
          ]

Testing on the sample provided in the question yields: