Giải thích các bước giải:
\[\begin{array}{l}
\frac{1}{x} + \frac{1}{{x + 7}} + \frac{{x - 7}}{{{x^2} + 7x}}\\
= \frac{1}{x} + \frac{1}{{x + 7}} + \frac{{x - 7}}{{x\left( {x + 7} \right)}}\\
= \frac{{x + 7}}{{x\left( {x + 7} \right)}} + \frac{x}{{x\left( {x + 7} \right)}} + \frac{{x - 7}}{{x\left( {x + 7} \right)}} = \frac{{x + 7 + x + x - 7}}{{x\left( {x + 7} \right)}} = \frac{{3x}}{{x\left( {x + 7} \right)}} = \frac{3}{{x + 7}}
\end{array}\]
