\(a,\left(x+6\right)\left(x-3\right)=2\left(x-3\right)\)
\(\Leftrightarrow\left(x+6\right)\left(x-3\right)-2\left(x-3\right)=0\)
\(\Leftrightarrow\left(x-3\right)\left(x+6-2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-3=0\\x+4=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=3\\x=-4\end{matrix}\right.\)
\(b,x^2+5x+6=0\)
\(\Leftrightarrow x^2+2x+3x+6=0\)
\(\Leftrightarrow x\left(x+2\right)+3\left(x+2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x+2=0\\x+3=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-2\\x=-3\end{matrix}\right.\)
\(c,\left(x-1\right)^2=0\)
\(\Leftrightarrow x-1=0\)
\(\Leftrightarrow x=1\)
\(d,\dfrac{x+1}{x-3}-\dfrac{41}{x+3}+\dfrac{x^2-3}{9-x^2}=0\left(dkxd:x\ne\pm3\right)\)
\(\Leftrightarrow\dfrac{x+1}{x-3}-\dfrac{41}{x+3}-\dfrac{x^2-3}{x^2-9}\)\(=0\)
\(\Leftrightarrow\left(x+1\right)\left(x+3\right)-41\left(x-3\right)-x^2+3=0\)
\(\Leftrightarrow x^2+4x+3-41x+123-x^2+3=0\)
\(\Leftrightarrow-37x=-129\)
\(\Leftrightarrow x=\dfrac{129}{37}\left(n\right)\)
