1. When $m=-\frac{1}{6}$, the value of the algebraic expression
$$
\frac{21-5 m}{m^{2}-9}-\frac{m}{m^{2}-9} \div \frac{m}{m+3}-\frac{m-3}{m+3}
$$

is ( ).
(A) -1
(B) $-\frac{1}{2}$
(C) $\frac{1}{2}$
(D) 1
1. A.

When $m \neq \pm 3$, the given algebraic expression is meaningful. Then
$$
\begin{array}{l}
\frac{21-5 m}{m^{2}-9}-\frac{m}{m^{2}-9} \div \frac{m}{m+3}-\frac{m-3}{m+3} \\
=\frac{21-5 m}{m^{2}-9}-\frac{m+3}{m^{2}-9}-\frac{m-3}{m+3} \\
=\frac{21-5 m-m-3-m^{2}+6 m-9}{m^{2}-9} \\
=\frac{9-m^{2}}{m^{2}-9}=-1 .
\end{array}
$$

Since $m=-\frac{1}{6}$ is within the allowed range of values for this algebraic expression, substituting it yields a result of -1.