Cho biểu thức: \({\rm{P  =  }}(\frac{1}{{x - 1}} + \frac{1}{{{x^2} - x}}):\frac{{x + 1}}{{{{(x - 1)}^2}}}\)a.

1a. Điều kiện: \(x \ne 0;x \ne 1;x \ne  - 1\)

\(\begin{array}{l}
{\rm{P}} = (\frac{1}{{x - 1}} + \frac{1}{{{x^2} - x}}):\frac{{x + 1}}{{{{(x - 1)}^2}}} = \left[ {\frac{x}{{x(x - 1)}} + \frac{1}{{x(x - 1)}}} \right]:\frac{{x + 1}}{{{{(x - 1)}^2}}}\\
 = \frac{{x + 1}}{{x(x - 1)}}.\frac{{{{(x - 1)}^2}}}{{x + 1}}\\
 = \frac{{x - 1}}{x}
\end{array}\)

b. \({\rm{P}} = \frac{2}{3} \Leftrightarrow \frac{{x - 1}}{x} = \frac{2}{3} \Leftrightarrow 3x - 3 = 2{\rm{x}} \Leftrightarrow x = {\rm{3 (t/m)}}\)