<s>[INST] Find the function and domain for $ (f\circ f)$ when $ f(x) = x+ \frac {1} {x} \ $ Find the function and domain for $ (f\circ f)$ 
My answer is $ \frac {x^4+3x^2+1x} {(x^2+1)(x)}?$
However, the program I am using states I am wrong. What have I done incorrectly? 
 [/INST] $$f(x) = x + \frac 1x = \frac {x^2+1}{x}$$
$$f(f(x)) = \frac{x^2 + 1}{x} + \frac{1}{\frac{x^2+1}x} = \frac{x^2+1}{x} + \frac{x}{x^2+1} = \frac{(x^2+1)^2 + x^2}{x(x^2+1)} = \frac{x^4 + 3x^2 + 1}{x(x^2 + 1)}$$
Domain: All $x \in \mathbb R$ such that $x\neq 0.$ (The denominator is undefined only when $x = 0.)$ $$(-\infty, 0)\cup (0, +\infty)$$ 
Note that $x^2 + 1 \gt 0\;\; \forall x \in \mathbb R$. 
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