[{(x-y)^2-z^2}/{(x+y)^2-z^2}]*[(x+y-z)/(x-y+z)]
Do you mean:
$\displaystyle \frac{(x-y)^{2}-z^2}{(x+y)^{2}-z^2} \times \frac{(x+y-z)}{(x-y+z)}$ ???
If so, use $\displaystyle {a^2} - {b^2} = (a+b) (a-b)$ to write $\displaystyle (x-y)^{2}-z^2 = (x-y-z)(x-y+z)$.
do the same for the denominator and cancel out like terms!
you may want to look at this
http://www.wolframalpha.com/input/?i=[{(x-y)^2-z^2}%2F{(x%2By)^2-z^2}]*[(x%2By-z)%2F(x-y%2Bz)]
doesn't look like its going to simplify too much... that is if OP is correct..