How do you write the mixed expression (h-3)/(h+5)-(h+2) as a rational expression?

$- \frac{{h}^{2} + 6 h + 13}{h + 5}$
$\frac{h - 3}{h + 5} - \left(h + 2\right)$
$= \frac{h - 3}{h + 5} - \left(h + 2\right) \cdot \frac{h + 5}{h + 5}$
$= \frac{\left(h - 3\right) - \left({h}^{2} + 7 h + 10\right)}{h + 5}$
$= - \frac{{h}^{2} + 6 h + 13}{h + 5}$