Giải thích các bước giải:
a,
ĐKXĐ: \(\begin{array}{l}
\\
\left\{ \begin{array}{l}
{x^2} - 9 \ne 0\\
x + 3 \ne 0\\
x - 3 \ne 0
\end{array} \right. \Leftrightarrow x \ne \pm 3
\end{array}\)
b,
Ta có:
\(\begin{array}{l}
M = \frac{{3x + 21}}{{{x^2} - 9}} + \frac{2}{{x + 3}} - \frac{3}{{x - 3}}\\
= \frac{{3x + 21}}{{\left( {x - 3} \right)\left( {x + 3} \right)}} + \frac{{2\left( {x - 3} \right)}}{{\left( {x - 3} \right)\left( {x + 3} \right)}} - \frac{{3\left( {x + 3} \right)}}{{\left( {x - 3} \right)\left( {x + 3} \right)}}\\
= \frac{{3x + 21 + 2\left( {x - 3} \right) - 3\left( {x + 3} \right)}}{{\left( {x - 3} \right)\left( {x + 3} \right)}}\\
= \frac{{3x + 21 + 2x - 6 - 3x - 9}}{{\left( {x - 3} \right)\left( {x + 3} \right)}}\\
= \frac{{2x + 6}}{{\left( {x - 3} \right)\left( {x + 3} \right)}}\\
= \frac{2}{{x - 3}}
\end{array}\)
c,
Thay \(x = \frac{1}{2}\) vào A ta được:
\[A = \frac{2}{{\frac{1}{2} - 3}} = \frac{2}{{ - \frac{5}{2}}} = - \frac{4}{5}\]
