If $$x + \frac{1}{{x + 1}} = 1,$$    then $${\left( {x + 1} \right)^5}$$   + $$\frac{1}{{{{\left( {x + 1} \right)}^5}}}$$   equals?

$$\eqalign{ & x + \frac{1}{{x + 1}} = 1 \cr & {\text{Adding both 1 sides}} \cr & \Rightarrow x + 1 + \frac{1}{{x + 1}} = 1 + 1 \cr & \Rightarrow \left( {x + 1} \right) + \frac{1}{{\left( {x + 1} \right)}} = 2 \cr & {\text{Put }}x + 1 = 1 \cr & {\text{And }}\frac{1}{{x + 1}} = 1 \cr & \therefore {\left( {x + 1} \right)^5}{\text{ + }}\frac{1}{{{{\left( {x + 1} \right)}^5}}} \cr & = 1 + 1 \cr & = 2 \cr} $$