$\frac{\sqrt{2x-3}}{\sqrt{x-1}}=2(DK:x> 1)\\\Leftrightarrow \sqrt{2x-3}=2.\sqrt{x-1}\\\Leftrightarrow \sqrt{2x-3}=\sqrt{4(x-1)}\\\Leftrightarrow (\sqrt{2x-3})^2=(\sqrt{4x-4})^2\\\Leftrightarrow 2x-3=4x-4\\\Leftrightarrow 2x-4x=-4+3\\\Leftrightarrow -2x=-1\\\Leftrightarrow x=\frac{1}{2}(KTMDK)$
Vậy pt vô nghiệm
1. $\frac{\sqrt{80xy^2}}{\sqrt{125x}}\\=\sqrt{\frac{80xy^2}{125x}}\\=\sqrt{\frac{16y^2}{25}}\\=\frac{\left | 4y \right |}{\left | 5 \right |}\\=\frac{-4y}{5}$(Vì y<0)
2.$\frac{3-\sqrt{3}}{\sqrt{3}}\\=\frac{(3-\sqrt{3}).\sqrt{3}}{\sqrt{3}.\sqrt{3}}\\=\frac{3\sqrt{3}-3}{3}\\=\frac{3(\sqrt{3}-1)}{3}\\=\sqrt{3}-1$
4.$\frac{\sqrt{9-4\sqrt{5}}}{2-\sqrt{5}}\\=\frac{\sqrt{(\sqrt{5})^2-2.\sqrt{5}.2+2^2}}{2-\sqrt{5}}\\=\frac{\sqrt{(\sqrt{5}-2)^2}}{2-\sqrt{5}}\\=\frac{\sqrt{5}-2}{2-\sqrt{5}}=-\frac{2-\sqrt{5}}{2-\sqrt{5}}=-1$