a) \(\frac{\sqrt{2x-3}}{x-1}=2\)
\(\Leftrightarrow\left(\frac{\sqrt{2x-3}}{x-1}\right)^2=4\)
\(\Leftrightarrow2x-3=4\left(x-1\right)^2\)
\(\Leftrightarrow2x-3=4\left(x^2-2x+1\right)\)
\(\Leftrightarrow2x-3-4x^2+8x-4=0\)
\(\Leftrightarrow-4x^2+10x-7=0\)
\(\Leftrightarrow-\left[\left(2x^2\right)-2.2x.\frac{10}{4}+\left(\frac{10}{4}\right)^2-18\right]=0\)
\(\Leftrightarrow-\left(2x-\frac{10}{4}\right)^2+18=0\)
\(\Leftrightarrow\left(\sqrt{18}\right)^2-\left(2x-\frac{10}{4}\right)^2=0\)
\(\Leftrightarrow\left(\sqrt{18}-2x-\frac{10}{4}\right)\left(\sqrt{18}+2x-\frac{10}{4}\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}\sqrt{18}-2x-\frac{10}{4}=0\\\sqrt{18}+2x-\frac{10}{4}=0\end{cases}\Leftrightarrow}\orbr{\begin{cases}-2x=\frac{10}{4}-\sqrt{18}\\2x=\frac{10}{4}-\sqrt{18}\end{cases}\Leftrightarrow\orbr{\begin{cases}x=\frac{-5+6\sqrt{2}}{4}\\x=\frac{5+6\sqrt{2}}{4}\end{cases}}}\)
