a) \(x\left(x-2017\right)=x-2017\)
\(\Rightarrow x\left(x-2017\right)-\left(x-2017\right)=0\\ \Rightarrow\left(x-1\right)\left(x-2017\right)=0\\ \Rightarrow\left[{}\begin{matrix}x-1=0\\x-2017=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=1\\x=2017\end{matrix}\right.\)
b) \(5x\left(x-1\right)=1-x\)
\(\Rightarrow5x\left(x-1\right)=-\left(x-1\right)\\ \Rightarrow5x\left(x-1\right)+\left(x-1\right)=0\\ \Rightarrow\left(5x+1\right)\left(x-1\right)=0\\ \Rightarrow\left[{}\begin{matrix}5x+1=0\\x-1=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=\dfrac{-1}{5}\\x=1\end{matrix}\right.\)
c) \(\left(3x-4\right)^2-\left(x+1\right)^2=0\)
\(\Rightarrow\left(3x-4-x-1\right)\left(3x-4+x+1\right)=0\\ \Rightarrow\left(2x-5\right)\left(4x-3\right)=0\\ \Rightarrow\left[{}\begin{matrix}2x-5=0\\4x-3=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=\dfrac{5}{2}\\x=\dfrac{3}{4}\end{matrix}\right.\)