Answer
The rational expression is improper. To make it proper,
$\displaystyle \frac{x(x-1)}{(x+4)(x-3)}=1+\frac{-2(x-6)}{(x+4)(x-3)}$
Work Step by Step
The rational expression $\displaystyle \frac{P}{Q}$ is called proper if
the degree of the polynomial in the numerator is less than the degree of the polynomial in the denominator.
Otherwise, the rational expression is called improper.
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The degree of the numerator is $2$, and
the degree of the denominator is $2$.
The rational expression is improper.
To make it proper,
$\displaystyle \frac{x(x-1)}{(x+4)(x-3)} =\frac{x^{2}-x}{x^{2}+x-12}$
$=\displaystyle \frac{(x^{2}+x-12) -2x+12}{x^{2}+x-12}$
$=\displaystyle \frac{(x^{2}+x-12) }{x^{2}+x-12} + \frac{-2x+12}{x^{2}+x-12}$
$=1+\displaystyle \frac{-2(x-6)}{(x+4)(x-3)}$
