\(a,x^2\left(x-5\right)-4\left(x-5\right)=0\)
\(\Leftrightarrow\left(x-5\right)\left(x^2-4\right)=0\)
\(\Leftrightarrow\left(x-5\right)\left(x-2\right)\left(x+2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-5=0\\x-2=0\\x+2=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=5\\x=2\\x=-2\end{matrix}\right.\)
Vậy \(S=\left\{5;\pm2\right\}\)
\(b,\dfrac{x+3}{x-3}-\dfrac{3}{x\left(x-3\right)}=\dfrac{1}{x}\left(ĐKXĐ:x\ne3;x\ne0\right)\)
\(\Leftrightarrow\dfrac{x\left(x+3\right)}{x\left(x-3\right)}-\dfrac{3}{x\left(x-3\right)}-\dfrac{x-3}{x\left(x-3\right)}=0\)
\(\Leftrightarrow\dfrac{x^2+3x-3-x+3}{x\left(x-3\right)}=0\)
\(\Rightarrow x^2+2x=0\)
\(\Leftrightarrow x\left(x+2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\left(loại\right)\\x+2=0\end{matrix}\right.\)
\(\Leftrightarrow x=-2\left(tm\right)\)
Vậy \(S=\left\{-2\right\}\)