Solution
Given : $$ x + \frac{1}{x} = 99$$
To find : $$\frac{100x}{2x^2 + 102x + 2}$$
= $$\frac{50x}{x^2 + 1 + 51x}$$
Dividing numerator and denominator by $$x$$
= $$\frac{50}{x + \frac{1}{x} + 51}$$
Substituting value of $$(x + \frac{1}{x})$$, we get :
= $$\frac{50}{99 + 51} = \frac{50}{150}$$
= $$\frac{1}{3}$$
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