The value of 11 + 2 + 3 + 11 - 2 + 3 \, is:

Answer: Option C

$$\begin{array}{rl}& \frac{1}{1+\sqrt{2}+\sqrt{3}}+\frac{1}{1-\sqrt{2}+\sqrt{3}}\\ & \Rightarrow \frac{1}{1+\sqrt{3}+\sqrt{2}}+\frac{1}{1+\sqrt{3}-\sqrt{2}}\\ & \Rightarrow \frac{1+\sqrt{3}-\sqrt{2}+1+\sqrt{3}+\sqrt{2}}{{\left(1+\sqrt{3}\right)}^2-{\left(\sqrt{2}\right)}^2}\\ & \Rightarrow \frac{2+2\sqrt{3}}{4+2\sqrt{3}-2}\\ & \Rightarrow \frac{2+2\sqrt{3}}{2+2\sqrt{3}}\\ & \Rightarrow 1\end{array}$$