Đáp án:
a) \(m \ne 2\)
Giải thích các bước giải:
\(\begin{array}{l}
a)\dfrac{{mx + 1}}{{x - 1}} = 2\\
\to mx + 1 = 2x - 2\\
\to \left( {m - 2} \right)x = - 3\\
\to x = - \dfrac{3}{{m - 2}}\\
Ycbt \Leftrightarrow m - 2 \ne 0\\
\to m \ne 2\\
d)\dfrac{{m\left( {x - 2m} \right) + x - 2}}{{\left( {x - 2} \right)\left( {x - 2m} \right)}} = 1\\
\to mx - 2{m^2} + x - 2 = {x^2} - 2mx - 2x + 4m\\
\to {x^2} + \left( { - 3m - 3} \right)x + 4m + 2{m^2} + 2 = 0\\
Ycbt \to 9{m^2} + 18m + 9 - 4\left( {4m + 2{m^2} + 2} \right) > 0\\
\to 9{m^2} + 18m + 9 - 16m - 8{m^2} - 8 > 0\\
\to {m^2} + 2m + 1 > 0\\
\to {\left( {m + 1} \right)^2} > 0\\
\to m \ne - 1\\
f)\dfrac{{\left( {m + 1} \right)x + m - 2}}{{x + 3}} = m\\
\to \left( {m + 1} \right)x + m - 2 = mx + 3m\\
\to \left( {m + 1 - m} \right)x = 2m + 2\\
\to x = 2m + 2\\
KL:\forall m
\end{array}\)
