Đáp án:
\(m \in \emptyset \)
Giải thích các bước giải:
\(\begin{array}{l}
a)DK:\left\{ \begin{array}{l}
m - 3 \ne 0\\
{m^2} - \left( {m - 3} \right)\left( {m + 2} \right) > 0\\
\dfrac{{2m}}{{m - 3}} < 0\\
\dfrac{{m + 2}}{{m - 3}} > 0
\end{array} \right.\\
\to \left\{ \begin{array}{l}
m \ne 3\\
{m^2} - {m^2} + m + 6 > 0\\
0 < m < 3\\
\left[ \begin{array}{l}
m > 3\\
m < - 2
\end{array} \right.
\end{array} \right.\\
\to \left\{ \begin{array}{l}
m > - 6\\
0 < m < 3\\
\left[ \begin{array}{l}
m > 3\\
m < - 2
\end{array} \right.
\end{array} \right.\\
\to m \in \emptyset \\
b)DK:\left\{ \begin{array}{l}
m - 2 \ne 0\\
{m^2} - \left( {m - 2} \right)\left( {m + 2} \right) > 0\\
\dfrac{{2m}}{{m - 2}} < 0\\
\dfrac{{m + 2}}{{m - 2}} > 0
\end{array} \right.\\
\to \left\{ \begin{array}{l}
m \ne 2\\
{m^2} - {m^2} + 4 > 0\\
0 < m < 2\\
\left[ \begin{array}{l}
m > 2\\
m < - 2
\end{array} \right.
\end{array} \right.\\
\to m \in \emptyset \\
c)DK:\left\{ \begin{array}{l}
m \ne 0\\
{m^2} - 2m + 1 - m\left( {m - 2} \right) > 0\\
\dfrac{{2\left( {m - 1} \right)}}{m} < 0\\
\dfrac{{m - 2}}{m} > 0
\end{array} \right.\\
\to \left\{ \begin{array}{l}
m \ne 0\\
1 > 0\left( {ld} \right)\\
0 < m < 1\\
\left[ \begin{array}{l}
m > 2\\
m < 0
\end{array} \right.
\end{array} \right.\\
\to m \in \emptyset
\end{array}\)
