by Guest » Sun Sep 04, 2016 6:35 am
There are many ways you could use to simplify the expression, one such way is to use the substitution [tex]u=e^x[/tex]
So
[tex]\frac{e^x-e^{-x}}{e^{-x}+1}[/tex]
[tex]=\frac{u-\frac{1}{u}}{\frac{1}{u}+1}[/tex]
[tex]=\frac{(u-\frac{1}{u})\times u}{(\frac{1}{u}+1)\times u}[/tex]
[tex]=\frac{u^2-1}{1+u}[/tex]
[tex]=\frac{(u-1)(u+1)}{1+u}[/tex]
[tex]=u-1[/tex]
[tex]=e^x-1[/tex]
Hope this helped,
R. Baber.