F'(x) for x^2+x+1/x Choose best answer right away!

I think I'm just doing the algebra wrong, but could you show me how to find the derivative for this problem.

x^2+x+1
------------ this line is a division bar. :)
x

omg need ten pts!!!!!

hahaha

Use the quotient rule.

x (d/dx(x^2+x+1)) - x^2+x+1 (d/dx(x))
---------------------------------------…
x^2

x (2x+1) - x^2+x+1

2x^2+1 -x^2 + x+1

(x^2 +x+2) / x^2

Divide it out:

f(x) = (x²+x+1)/x = x + 1 + 1/x = x+1+x^(-1)

and differentiate it term by term
f'(x) = 1 + 0 - x^(-2) = 1 - 1/x² = (x²-1)/x²

or several other ways it could be arranged (x+1)(x-1)/x² for example