Lời giải:
a.
$A=\frac{3x+15}{(x-3)(x+3)}+\frac{x-3}{(x+3)(x-3)}-\frac{2(x+3)}{(x-3)(x+3)}$
$=\frac{3x+15+(x-3)-2(x+3)}{(x+3)(x-3)}=\frac{2x+6}{(x-3)(x+3)}$
$=\frac{2(x+3)}{(x-3)(x+3)}=\frac{2}{x-3}$
b.
Để $A=\frac{1}{2}$
$\Leftrightarrow \frac{2}{x-3}=\frac{1}{2}$
$\Leftrightarrow x-3=4$
$\Leftrightarrow x=7$ (tm)