I am evaluating the function $\displaystyle f(x)=x^2-x-lnx$

The derivative should be $\displaystyle f'(x)=2x-1-1/x$

I am trying to find the critical numbers:

$\displaystyle 0=2x-1-1/x$

Here comes my problem... I used two different methods but my results are different

Method one:

$\displaystyle 0=2x-1-1/x$

$\displaystyle 0=(2x^2/x)-(x/x)-(1/x)$ (common denominator)

$\displaystyle 0=(2x^2-x-1)/x$

And so on...

Method two:

$\displaystyle 0=2x-1-1/x$

$\displaystyle 1=2x-1/x$

$\displaystyle 1=(2x^2)/x-(1/x)$

$\displaystyle 1=(2x^2-1)/x$

$\displaystyle 1*x=(2x^2-1)$

$\displaystyle x=(2x^2-1)$

$\displaystyle 0=(2x^2-x-1)$

And so on...

When I nowcompare method one with method twoI see that$\displaystyle 0=(2x^2-x-1)/x$isdifferentfrom$\displaystyle 0=(2x^2-x-1)$. (Why is my result in method two not devided by x?)

My question is now, why? And what am I doing wrong? :/

Please help