`6)`

`a)(m^2-1)x+1-m=0`

`<=>(m^2-1)x=m-1`

`<=>(m+1)(m-1)x=m-1`

`<=>(m+1)x=0`

`<=>`\(\left[ \begin{array}{l}m+1=0\\x=0\end{array} \right.\) 

`<=>`\(\left[ \begin{array}{l}m=-1\\x=0\end{array} \right.\) 

`b)(m^2-4)x+2-m=0`

`<=>(m^2-4)=m-2`

`<=>(m+2)(m-2)x=m-2`

`<=>(m+2)x=0`

`<=>`\(\left[ \begin{array}{l}m+2=0\\x=0\end{array} \right.\) 

`<=>`\(\left[ \begin{array}{l}m=-2\\x=0\end{array} \right.\) 

`c)(m^2-9)x+3-m=0`

`<=>(m^2-9)x=m-3`

`<=>(m+3)(m-3)x=m-3`

`<=>(m+3)x=0`

`<=>` \(\left[ \begin{array}{l}m+3=0\\x=0\end{array} \right.\) 

`<=>`\(\left[ \begin{array}{l}m=-3\\x=0\end{array} \right.\) 

 `d)(m^2-16)x+4-m=0`

`<=>(m^2-16)=m-4`

`<=>(m-4)(m+4)x=m-4`

`<=>(m+4)x=0`

`<=>`\(\left[ \begin{array}{l}m+4=0\\x=0\end{array} \right.\)

`<=>`\(\left[ \begin{array}{l}m=-4\\x=0\end{array} \right.\)