How to simplify this symbolic equation - nominator and denominator manipulation

Hi,

I am solving well known equation:

syms c t tau
eq1 = (c*t)^2 == (c*tau)^2+(v*t)^2
solvedeq1=simplify((solve(eq1, t)))
solvedeq1(1)

Now the standard way of giving the answer is:

How do I manipulate MATLAB to give me this final form? I have tried randomly to apply all possible symbolic commands.

Thank you for your time.

Answer 1

[John D'Errico]

I never did understand why people worry about making a symbolic tool give a result in a mathematically identical form, that happens to look as you want to write it. Can you spend an hour figuring out how to produce a form that looks as you want? Probably. Why?

You want to solve this essentially in a non-dimensional form for v. So write the equation by dividing by c^2. We will use the transformation u = v/c.

syms c t tau v u
eq1 = (t)^2 == (tau)^2+(u*t)^2

eq1 = 

solvedeq1=simplify((solve(eq1, t)))

solvedeq1 = 

solvedeq1(2)

ans = 

Having done that, now undo the transformation, but do NOT use symplify which may screw things up.

subs(solvedeq1(2),u,v/c)

ans = 

Note that I had to use solvedeq1(2) to give the positive solution.

[Tomi Makkonen]

Thank you John.