If $$2 = x + \frac{1}{{1 + \frac{1}{{5 + \frac{1}{2}}}}},$$    then the value of x is equal to:

A. $$\frac{{14}}{{13}}$$

B. $$1$$

C. $$\frac{{13}}{{15}}$$

D. $$\frac{{15}}{{13}}$$

Answer: Option D

Solution(By Examveda Team)

$$\eqalign{ & 2 = x + \frac{1}{{1 + \frac{1}{{5 + \frac{1}{2}}}}} \cr & 2 = x + \frac{1}{{1 + \frac{1}{{\frac{{11}}{2}}}}} \cr & 2 = x + \frac{1}{{\frac{{11 + 2}}{{11}}}} \cr & 2 = x + \frac{{11}}{{13}} \cr & 2 - \frac{{11}}{{13}} = x \cr & x = \frac{{15}}{{13}} \cr} $$