HD:⟺√x−(x−1)+√3−x−(x−2)=x2−3x+1⟺−(x2−3x+1)√x+x−1+−(x2−3x+1)√3−x+x−2=x2−3x+1⟺(x2−3x+1)[1√x+x−1+1√3−x+x−2+1]=0⟺....
HD:$pt \iff \sqrt{x}-(x-1)+\sqrt{3-x}-(x-2)=x^2-3x+1⟺−(x2−3x+1)√x+x−1+−(x2−3x+1)√3−x+x−2=x2−3x+1\iff (x^2-3x+1)\left[ \dfrac{1}{\sqrt{x}+x-1}+\dfrac{1}{\sqrt{3-x}+x-2}+1\right]=0 $$\iff ....$