Therefore: f (x) = (x 2-1)/(x-1)+1/(x-1).

=x+ 1+ 1/(x- 1)

=(x- 1)+ 1/(x- 1)+2

From the basic inequality: f (x) >; =4, the equal sign is true if and only if x=2.

2、f(x)= 1/(x+ 1/x)

Because: x+1/x > =2

So: f (x) < = 1/2

So the maximum value of f(x) is 0.5, and the equal sign holds if and only if x= 1.