Solution
$$x+\frac{1}{x}=99$$
$$x^{2}+1=99x$$
multiply with 2 on both sides
$$2x^{2}+2=198x$$
add 102x on both sides,
$$2x^{2}+2+102x=198x+102x$$
$$2x^{2}+2+102x=300x$$
$$2x^{2}+2+102x=3\times100x$$
$$\frac{2x^{2}+102x+2}{100x}=3$$
$$\frac{100x}{2x^{2}+102x+2}=\frac{1}{3}$$
so the answer is option C.
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