Factor[(z^2-1)/(z^2+1)+(z^4-1)/(z^4+1)(z^6-1)/(z^6+1)(z^8-1)/(z^8+1)]

Uh oh! Wolfram|Alpha doesn't run without JavaScript.

Please enable JavaScript. If you don't know how, you can find instructionshere.Once you've done that, refresh this page to start using Wolfram|Alpha.