#Limits 2

$\large \begin{aligned} L & = \lim_{x \to 1} \left(\frac {1+x}{2+x} \right)^{\frac {1-\sqrt x}{\color{#3D99F6}1-x}} \\ & = \lim_{x \to 1} \left(\frac {1+x}{2+x} \right)^{\frac {1-\sqrt x}{\color{#3D99F6}(1-\sqrt x)(1+\sqrt x)}} \\ & = \lim_{x \to 1} \left(\frac {1+x}{2+x} \right)^{\frac 1{1+\sqrt x}} \\ & = \left(\frac 23 \right)^\frac 12 \\ & = \sqrt{\frac 23} \end{aligned}$

$\implies a + b + n = 2+3+2 = \boxed{7}$

I solved It mentally: the only problem is at the exponent but it is in the form (1-x)/(1-x^2) and by semplify and substituting we get to (2/3)^ 1/2 2+2+3=7