The reciprocal of $$x+\frac{1}{x}$$
$$x+\frac{1}{x}$$
$$=\frac{x^{2}+1}{x}$$
Reciprocal of $$x+\frac{1}{x}$$
$$=$$Reciprocal of $$\frac{x^{2}+1}{x}$$
$$=\frac{1}{\frac{x^{2}+1}{x}}$$
$$=\frac{x}{x^{2}+1}$$
Hence, Option A is Correct.
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