f(x)=x+(1/x), find f(f(x)). I am stuck on how to solve it. Please help me.

What I did so far was:
(X+(1/x))+(1/(x+1/x))
I then get confused what to do. Would I multiply x into each equation to get rid of the fraction so it would look like this:
(X^2+1)+(1/(x^2+1))
Or do I turn them into a fraction so would be:
((X^2+1)/x)+(1/((x^2+1)/x))
Or am I doing it completely wrong?

Question

f(x)=x+(1/x), find f(f(x)). I am stuck on how to solve it. Please help me.

What I did so far was:
(X+(1/x))+(1/(x+1/x))
I then get confused what to do. Would I multiply x into each equation to get rid of the fraction so it would look like this:
(X^2+1)+(1/(x^2+1))
Or do I turn them into a fraction so would be:
((X^2+1)/x)+(1/((x^2+1)/x))
Or am I doing it completely wrong?

hartnn · Answer

((X^2+1)/x)+(1/((x^2+1)/x)) is correct

=((X^2+1)/x)+(x/((x^2+1)))

anonymous · Answer

Thank you