If $$2x + \frac{1}{{3x}} = 5{\text{,}}$$   then the value of $$\frac{{5x}}{{6{x^2} + 20x + 1}}$$   is?

Solution (By Examveda Team)

$$\eqalign{ & 2x + \frac{1}{{3x}} = 5 \cr & 6{x^2}{\text{ + 1 = 15x}}\,......{\text{(i)}} \cr & {\text{Now,}}\frac{{5x}}{{6{x^2} + 20x + 1}} \cr & = \frac{{5x}}{{6{x^2} + 1 + 20x}} \cr & \left[ {{\text{From equation (i)}}} \right] \cr & = \frac{{5x}}{{15x + 20x}}{\text{ }} \cr & = \frac{{5x}}{{35x}} \cr & = \frac{1}{7} \cr} $$