If $$x=\frac{1}{2+\sqrt{3}}$$ and $$y=\frac{1}{2-\sqrt{3}}$$ then the value of $$\frac{1}{x+1} + \frac{1}{y+1}$$ is

$$x=\frac{1}{2+\sqrt{3}}$$ , on rationalizing x = 2 - $$\surd3$$

$$y=\frac{1}{2-\sqrt{3}}$$ , on rationalizing y = 2 + $$\surd3$$

we need to find value of $$\frac{1}{x+1} + \frac{1}{y+1}$$

using above values of x and y

$$\frac{1}{x+1} + \frac{1}{y+1}$$ = $$\frac{1}{2 + \surd3 +1} + \frac{1}{2 - \surd3 +1}$$

now on rationalizing ,

$$\frac{1}{x+1} + \frac{1}{y+1}$$ = $$\frac{3 - \surd3 + 3 + \surd3}{6}$$ = 1