The value of $$\frac{1}{1+\sqrt{2}+\sqrt{3}}+\frac{1}{1-\sqrt{2}+\sqrt{3}}$$ is:

Expression : $$\frac{1}{1+\sqrt{2}+\sqrt{3}}+\frac{1}{1-\sqrt{2}+\sqrt{3}}$$

Rationalizing the denominator, we get :

= $$(\frac{1}{1+\sqrt{3}+\sqrt{2}}\times\frac{1+\sqrt3-\sqrt2}{1+\sqrt3-\sqrt2})+(\frac{1}{1+\sqrt{3}-\sqrt{2}}\times\frac{1+\sqrt3+\sqrt2}{1+\sqrt3+\sqrt2})$$

= $$[\frac{1+\sqrt3-\sqrt2}{(1+\sqrt3)^2-(\sqrt2)^2}]+[\frac{1+\sqrt3+\sqrt2}{(1+\sqrt3)^2-(\sqrt2)^2}]$$

= $$\frac{(1+\sqrt3-\sqrt2)+(1+\sqrt3+\sqrt2)}{(1+3+2\sqrt3)-(2)}$$

= $$\frac{2+2\sqrt3}{2+2\sqrt3}=1$$

=> Ans - (A)