Giải thích các bước giải:
a,
Ta có:
\(\begin{array}{l}
P = \left( {\frac{x}{{{x^2} - 36}} - \frac{{x - 6}}{{{x^2} + 6x}}} \right):\frac{{2x - 6}}{{{x^2} + 6x}}\\
= \left( {\frac{x}{{\left( {x - 6} \right)\left( {x + 6} \right)}} - \frac{{x - 6}}{{x\left( {x + 6} \right)}}} \right):\frac{{2x - 6}}{{x\left( {x + 6} \right)}}\\
= \frac{{x.x - \left( {x - 6} \right)\left( {x - 6} \right)}}{{x\left( {x - 6} \right)\left( {x + 6} \right)}}.\frac{{x\left( {x + 6} \right)}}{{2x - 6}}\\
= \frac{{{x^2} - {x^2} + 12x - 36}}{{x - 6}}.\frac{1}{{2\left( {x - 3} \right)}}\\
= \frac{{12\left( {x - 3} \right)}}{{x - 6}}.\frac{1}{{2\left( {x - 3} \right)}}\\
= \frac{6}{{x - 6}}
\end{array}\)
b,
\(P = 1 \Leftrightarrow \frac{6}{{x - 6}} = 1 \Leftrightarrow x - 6 = 6 \Leftrightarrow x = 12\left( {t/m} \right)\)
c,
\(P < 0 \Leftrightarrow \frac{6}{{x - 6}} < 0 \Leftrightarrow x - 6 < 0 \Rightarrow x < 6\)
