$A =\dfrac{x+2}{x+3} -\dfrac{5}{x^2 + x-6} +\dfrac{1}{2-x}$
a) $ĐKXĐ:\, x^2 - x-6\ne 0\Leftrightarrow \begin{cases}x \ne 2\\x \ne -3\end{cases}$
b) $A =\dfrac{(x+2)(x-2)}{(x+3)(x-2)} -\dfrac{5}{(x+3)(x-2)} -\dfrac{x+3}{(x+3)(x-2)}$
$\to A =\dfrac{x^2 - 4 - 5 - (x+3)}{(x+3)(x-2)}$
$\to A =\dfrac{x^2 - x - 12}{(x+3)(x-2)}$
$\to A =\dfrac{(x+3)(x-4)}{(x+3)(x-2)}$
$\to A =\dfrac{x-4}{x-2}$
c) $A=-\dfrac34$
$\to \dfrac{x-4}{x-2}=-\dfrac34$
$\to 4(x-4)=-3(x-2)$
$\to 4x -16 = -3x +6$
$\to 7x = 22$
$\to x =\dfrac{22}{7}$