\inline (X+1)\left [ \sqrt{X+1}-1 \right ]-(X-1)\left[ \sqrt{X+2}-2 \right ]=0 \Leftrightarrow(X+1)\left [ \frac{X-2}{\sqrt{X+1}+1} \right ]-(X+1)\left [ \frac{X-2}{\sqrt{X+2}-2} \right ]=0 \Leftrightarrow (X-2)(\frac{X+1}{\sqrt{X-1}+1}-\frac{X-1}{\sqrt{X+2}-2})=0 \Rightarrow X=2