If x + 1/x = 99 , find the value of 100x2x^2 + 2 + 102x is?

Answer: Option C

$$\begin{array}{rl}& x+\frac{1}{x}=99\\ & \therefore x^2+1=99x\\ & \Rightarrow 2\left(x^2+1\right)=2\times 99x\\ & \Rightarrow 2x^2+2=198x\\ & =\frac{100x}{2x^2+2+102x}\\ & =\frac{100x}{198x+102x}\\ & =\frac{100x}{300x}\\ & =\frac{1}{3}\end{array}$$