Question: check whether two expressions are equivalent or identical, resp.?

I try to find out, whether two expressions are equvalent or identical, respectively.
E.g. I have the following expressions:

m1 := -sigma^2*n*(phi+ln(-1/(-exp(phi)+exp(phi)*mu/n-mu/n)))/(mu*(-1+mu/n)*phi);
m2 := 2*mu*n*(phi+ln(-1/(-exp(phi)+(1/2)*exp(phi)*(n+sqrt(n^2-4*n*sigma^2))/n-(1/2)*(n+sqrt(n^2-4*n*sigma^2))/n)))/((n+sqrt(n^2-4*n*sigma^2))*phi);


and I tried to just subtract one from the other and afterwards simplify:


If m1=m2, then this has to equal zero, right?
In any case I have doubts, that this always leads to the right conclusion.

Can anyone help?



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