If 5x2x^2 + 5x + 1 = 1/3, then the value of ( x + 12x ) = \,?

Answer: Option D

$$\begin{array}{rl}& \frac{5x}{2x^2+5x+1}=\frac{1}{3}\\ & \Rightarrow \frac{5}{\frac{2x^2}{x}+\frac{5x}{x}+\frac{1}{x}}=\frac{1}{3}\\ & \Rightarrow \frac{5}{2x+\frac{1}{x}+5}=\frac{1}{3}\\ & \Rightarrow 2x+\frac{1}{x}+5=15\\ & \Rightarrow 2x+\frac{1}{x}=10\\ & \text{Divide by 2 both sides }\\ & \Rightarrow x+\frac{1}{2x}=\frac{10}{2}\\ & \Rightarrow 2x+\frac{1}{x}=5\end{array}$$