1) \(\left(2x-3\right)^2-\left(x-1\right)^2=0\)
\(\Leftrightarrow\left(2x-3-x+1\right)\left(2x-3+x-1\right)=0\)
\(\Leftrightarrow\left(x-2\right)\left(3x-4\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-2=0\\3x-4=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=2\\3x=4\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=2\\x=\dfrac{4}{3}\end{matrix}\right.\)
4) \(\left(x+2\right)^2-\left(2x-5\right)^2=0\)
\(\Leftrightarrow\left(x+2-2x+5\right)\left(x+2+2x-5\right)=0\)
\(\Leftrightarrow\left(7-x\right)\left(3x-3\right)=0\)
\(\Leftrightarrow3\left(7-x\right)\left(x-1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}7-x=0\\x-1=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=7\\x=1\end{matrix}\right.\)
7) \(\left(3x-4\right)^2-\left(x+2\right)^2=0\)
\(\Leftrightarrow\left(3x-4-x-2\right)\left(3x-4+x+2\right)=0\)
\(\Leftrightarrow\left(2x-6\right)\left(4x-2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}2x-6=0\\4x-2=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}2x=6\\4x=2\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{6}{2}\\x=\dfrac{2}{4}\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=3\\x=\dfrac{1}{2}\end{matrix}\right.\)
