\[\begin{array}{l}
y = \frac{{x + 1}}{{{x^2} - 2x + m}}\\
DK:\,\,\,{x^2} - 2x + m \ne 0\\
Do\,\,thi\,\,ham\,\,so\,\,co\,\,dung\,\,1\,\,tiem\,\,can\,\,dung\\
\Leftrightarrow pt\,\,g\left( x \right) = {x^2} - 2x + m = 0\,\,\,\,co\,\,\,nghiem\,\,\,kep\,\,x \ne - 1\,\,\,\,hoac\,\,\,\,co\,\,\,hai\,\,nghiem\,\,pb\,\,\,trong\,\,do\,\,co\,\,\,1\,\,nghiem\,\,\,x = - 1\\
TH1:\,\,\,pt\,\,{x^2} - 2x + m = 0\,\,\,\,co\,\,\,nghiem\,\,\,kep\,\,x \ne - 1\,\,\,\\
\Leftrightarrow \left\{ \begin{array}{l}
\Delta ' = 0\\
g\left( { - 1} \right) \ne 0
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
1 - m = 0\\
1 + 2 + m \ne 0
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
m = 1\\
m \ne - 3
\end{array} \right. \Leftrightarrow m = 1.\\
TH2:\,\,pt\,\,g\left( x \right) = {x^2} - 2x + m = 0\,\,co\,\,\,hai\,\,nghiem\,\,pb\,\,\,trong\,\,do\,\,co\,\,\,1\,\,nghiem\,\,\,x = - 1\\
\Leftrightarrow \left\{ \begin{array}{l}
\Delta ' > 0\\
g\left( { - 1} \right) = 0
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
1 - m > 0\\
3 + m = 0
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
m < 1\\
m = - 3
\end{array} \right. \Leftrightarrow m = - 3\\
Vay\,\,\,m = 1;\,\,m = - 3\,\,thoa\,\,man.
\end{array}\]
