Use MuPAD to prove $(4^{(x-1)}+2^{(2x-4)})/(2^{(2x+1)}+5\cdot(2^{(2x-3)}))=5/42$

Question

I attempted to answer this in the following way, but got stuck on being unable to cancel out $4^x$ and $2^{2x}$. Even though they are clearly mathematically the same, I failed to find a command that cancels these out in any of the expressions (I tried expand, combine, simplify and normal, in various combinations but could not find the command that would accomplish this). I resorted to a "manual" substitution but it is clearly not the correct way to answer this question. Any suggestions to manipulate the expression to achieve the desired outcome would be welcome.

a:=((4^(x-1)+2^(2*x-4))/(2^(2*x+1)+5*(2^(2*x-3))));

                          x - 1    2 x - 4
                         4      + 2
                       ---------------------
                        2 x + 1      2 x - 3
                       2        + 5 2

b:=expand(a);

                              x       2 x
                           2 4       2
                         ------- + -------
                             2 x       2 x
                         21 2      42 2

c:=subs(b,4^x=2^(2*x));

                                  2 x
                               5 2
                              -------
                                  2 x
                              42 2

simplify(c);

                               5/42