Given f(x)= [sqrt(x^2 +1) + x] / x and x>0

Solution is f(x) = sqrt[1 + (1/x^2)] +1

Can someone show we the way how to get there?

I did:

f(x)= [sqrt(x^2 +1) + x] / x

= sqrt(x^2 +1) /x + x/x

= sqrt(x^2 +1) /x + 1

But I stuck with the first term.

Thanks for any help