[tex]\sqrt{x^{2}+x-5}-1+\sqrt{-x^{2}+x+3}-1-x^{2}+3x-2=\frac{x^{2}+x-6}{\sqrt{x^{2}+x-5}+1}+\frac{-x^{2}+x+2}{\sqrt{-x^{2}+x+3}+1}-(x-2)(x-1)=\frac{(x-2).(x+3)}{\sqrt{x^{2}+x-5}+1}+\frac{-(x-2).(x+1)}{\sqrt{-x^{2}+x+3}+1}-(x-2)(x-1)=(x-2)(\frac{x+3}{\sqrt{x^{2}+x-5}+1}-\frac{x+1}{\sqrt{-x^{2}+x+3}+1}+1-x)=0[/tex]