Đáp án:
\[M = - 1\]
Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
M = \left( {\frac{1}{x} + \frac{1}{y}} \right):\frac{{x + y}}{{xy}} + \frac{y}{{x - y}} - \frac{{5 - x}}{{y - x}}\\
= \frac{{x + y}}{{xy}}.\frac{{xy}}{{x + y}} + \frac{{y + 5 - x}}{{x - y}}\\
= 1 + \frac{{5 - \left( {x - y} \right)}}{{x - y}}\\
= 1 + \frac{5}{{x - y}} - 1\\
= \frac{5}{{x - y}}
\end{array}\)
Lại có:
\(\begin{array}{l}
{\left( {x + 1} \right)^2} + {\left( {y - 4} \right)^2} = 0\\
\Leftrightarrow \left\{ \begin{array}{l}
{\left( {x + 1} \right)^2} = 0\\
{\left( {y - 4} \right)^2} = 0
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
x = - 1\\
y = 4
\end{array} \right.
\end{array}\)
Do đó, \(M = \frac{5}{{x - y}} = \frac{5}{{ - 1 - 4}} = \frac{5}{{ - 5}} = - 1\)
