Giải và biện luận các phương trình sau theo \(m\):
1) \(3(m+1)x+4=2x+5m+5\)     (1)
2) \(m^{2}(x+1)=x+m\)             (2)
1) Ta có:
(1) \(\Leftrightarrow (3m+1)x=5m+1\)
\(3m+1\neq 0  \Leftrightarrow m\neq -\frac{1}{3}\), thì (1) \(\Leftrightarrow x=\frac{5m+1}{3m+1}\)
\(3m+1= 0 \Leftrightarrow m= -\frac{1}{3}\) ta có (1) \(\Leftrightarrow 0x=5(-\frac{1}{3})+1=-\frac{2}{3}\Rightarrow \)VN

2) Ta có:
(2) \(\Leftrightarrow (m^{2}-1)x=m-m^{2} \Leftrightarrow  (m-1)(m+1)x=m(1-m)\)
\(m\neq \pm 1\) thì (1)\(\Leftrightarrow x=\frac{-m}{m+1}\).
\(m=1\)     thì (1)\(\Leftrightarrow 0x=0\) vô số nghiệm.
\(m=-1\) thì (1)\(\Leftrightarrow 0x=(-1)[1+1]=-2\) vô nghiệm
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