If $$4x + \frac{1}{x} = 5,$$   $$x \ne 0{\text{,}}$$   then the value of $$\frac{{5x}}{{4{x^2} + 10x + 1}}$$    is?

Solution (By Examveda Team)

$$\eqalign{ & \frac{{5x}}{{4{x^2} + 10x + 1}} \cr & = \frac{5x}{{x\left( {4x + 10 + \frac{1}{x}} \right)}} \cr & = \frac{5}{{4x + \frac{1}{x} + 10}} \cr & = \frac{5}{{5 + 10}} \cr & = \frac{5}{{15}} \cr & = \frac{1}{3} \cr} $$