Symbolic engine - strange results

You wouldn't expect the two results you show as expected. A variable K shouldn't change to the unit Kelvin, a variable m should change to the unit metre. But this is due to the fact that you typed in these expressions, and Prime's famous autolabelling feature assumed that K and m are units, and turns them blue.

You should also know that the symbolic processor doesn't 'know' about units. At best it treats them like unknown variables.

Apart from that, and to your actual question:

What if you add 'simplify' to the symbolic evaluation?

And additionally: You are using Prime 6, where you have the option to choose between two symbolic solvers: The 'new' one , which is the default, or the former one (MuPad). Do they both give the same answer?

Finally: It is known for a long time, with Mathcad as well as Prime, that the output of the symbolic solver is hard to control. There are few options for that. Here's the output for Mathcad 11 (which uses yet another symbolic processor (Maple):

Success!
Luc

You are not doing anything wrong.

Controlling the the way an output from the symbolic is displayed is hard to impossible. In Mathcad/Prime we don't have many options to do so. You may use additionally "simplify", "simplify,max", "factor", "expand", "collect,..." or the like (sometimes with unexpected results) but in general you'll have to accept the output as is.

You should also consider that in math a fraction is considered "simplified" when the denominator is rational. So in math often roots are not desired in the denominator. Eliminating them often makes the term a bit less compact as in your case and the new symbolic seems to automatically default to this kind of simplification.

I see no way to convince the new symbolic engine in Prime 6 to display the result the way you'd like it to see.

The symbolic not even considers that m may be zero an so its result would not be correct.

In Prime 6 you have the option to switch back to the prior, legacy symbolic engine (muPad, not available any more in version 7 of Prime). This engine is aware of the possible m=0 problem and displays the result similar to the one you'd like to see and, on the other hand,  it seems not to be able to talk it into displaying it with a rational denominator 😉