Solve Equations in Mathematica using Solve, FindRoot and Reduce

[DHAndrea666]

I really enjoyed watching your video and learnt so much from you! I have a question and wonder whether you could help me. I tried prove that x^(x/x-1))-x-1>0, where x>1. Do you know how I can accomplish that using Mathematica? I tried to plot it, it seems always above 0. I used FindRoot searching for values starting from 0.00001. It returns with a complex number. But how I can be sure about it??

I would really really appreciate if you could help me.

[arlenmalei]

@DHAndrea666

You wrote the wrong equation. Where is the first half of the brackets.

[DHAndrea666]

@arlenmalei

Sorry about the typo. I am trying to prove that x^(x/(x-1))-x-1>0. Any suggestionts?

[ch0c4]

Suddenly, my homework doesn't look so hard as it looked.