If $$x + \frac{1}{x} = 8,$$   then find the value of $$\frac{{5x}}{{{x^2} + 1 - 6x}}.$$

A. 2.5

B. 6

C. 5

D. 6.5

Answer: Option A

Solution(By Examveda Team)

$$\eqalign{ & x + \frac{1}{x} = 8 \cr & {x^2} + 1 = 8x \cr & \frac{{5x}}{{{x^2} + 1 - 6x}} \cr & = \frac{{5x}}{{8x - 6x}} \cr & = \frac{{5x}}{{2x}} \cr & = \frac{5}{2} \cr & = 2.5 \cr} $$