Rewrite

$\displaystyle \frac{{-{10}{x}^{{2}}+{17}{x}-{11}}}{{{2}{x}-{3}}}$

in the form

$\displaystyle {q}{\left({x}\right)}+\frac{{{r}{\left({x}\right)}}}{{{2}{x}-{3}}}$.

$\displaystyle -{10}{x}^{{2}}+{17}{x}-{11}$	$\displaystyle =$		$\displaystyle +$
$\displaystyle {2}{x}-{3}$				$\displaystyle {2}{x}-{3}$