a) \(\left\{ \begin{array}{l}{(2m - 1)^2} - 4({m^2} - m) \ge 0\\\dfrac{1}{{{m^2} - m}} > 0\\\dfrac{{2m - 1}}{{{m^2} - m}} > 0\end{array} \right.\) \( \Leftrightarrow \left\{ \begin{array}{l}1 \ge 0\\{m^2} - m > 0\\2m - 1 > 0\end{array} \right.\) \( \Leftrightarrow m > 1\)
b) \(\left\{ \begin{array}{l}{(m - 2)^2} - (m + 3)(m - 1) \ge 0\\\dfrac{{m - 2}}{{m + 3}} > 0\\\dfrac{{m - 1}}{{m + 3}} > 0\end{array} \right.\) \( \Leftrightarrow \left\{ \begin{array}{l} - 6m + 7 \ge 0\\(m - 2)(m + 3) < 0\\(m - 1)(m + 3) > 0\end{array} \right.\)\( \Leftrightarrow \left\{ \begin{array}{l}m \le \dfrac{7}{6}\\ - 3 < m < 2\\\left[ \begin{array}{l}m > 1\\m < - 3\end{array} \right.\end{array} \right. \Leftrightarrow 1 < m \le \dfrac{7}{6}\)
