$ \ \text{HD:}$$\iff \sqrt{x}-(x-1)+\sqrt{3-x}-(x-2)=x^2-3x+1$$\iff \dfrac{-(x^2-3x+1)}{\sqrt{x}+x-1}+\dfrac{-(x^2-3x+1)}{\sqrt{3-x}+x-2}=x^2-3x+1$$\iff (x^2-3x+1)\left[ \dfrac{1}{\sqrt{x}+x-1}+\dfrac{1}{\sqrt{3-x}+x-2}+1\right]=0 $$\iff ....$
$ \ \text{HD:}$$
pt \iff \sqrt{x}-(x-1)+\sqrt{3-x}-(x-2)=x^2-3x+1$$\iff \dfrac{-(x^2-3x+1)}{\sqrt{x}+x-1}+\dfrac{-(x^2-3x+1)}{\sqrt{3-x}+x-2}=x^2-3x+1$$\iff (x^2-3x+1)\left[ \dfrac{1}{\sqrt{x}+x-1}+\dfrac{1}{\sqrt{3-x}+x-2}+1\right]=0 $$\iff ....$