Consider the expression
expr = E^x Sqrt[1 - E^(-4 x)] - Sqrt[-E^(-2 x) + E^(2 x)]
At least for x>0
I would expect this to be equal to zero (because E^x
is manifestly positive, so that it should only influence the scale when both square roots are expressed in polar coordinates as a complex number). But if I try
Assuming[x > 0, expr // FullSimplify]
E^x Sqrt[1 - E^(-4 x)] - E^-x Sqrt[-1 + E^(4 x)]
The result is a bit disappointing. It should still be zero (one can even verify it by plotting some range of x>0
), but Mathematica does not seem to see it. How should I modify the command such that Mathematica properly returns zero after simplification?
FullSimplify[expr^2, x > 0]
works though. $\endgroup$expr
itself should be zero too. Basically, I am trying to understand what Mathematica gets hung up on here. To have a larger toolbox for more complicated/less obvious examples. $\endgroup$FullSimplify[ComplexExpand[expr], x>0]
$\endgroup$FullSimplify[ComplexExpand[expr], x>0]
simplify to zero? $\endgroup$