Answer
The simplified form of given expression = $\frac{11}{(x - 3)(x - 4)}$
Work Step by Step
$\frac{2x + 3}{x^{2} - 7x + 12}$ - $\frac{2}{x - 3}$
L.C.M of denominator terms ${x^{2} - 7x + 12}$ = (x - 3)(x - 4) and (x - 3) = (x - 3)(x - 4)
= $\frac{2x + 3 - 2(x - 4)}{(x - 3)(x - 4)}$
= $\frac{2x + 3 - 2x + 8}{(x - 3)(x - 4)}$
= $\frac{11}{(x - 3)(x - 4)}$
The simplified form of given expression = $\frac{11}{(x - 3)(x - 4)}$
