Answer
$\displaystyle \frac{x^{2}+5}{x^{2}-4}$ is improper,
$\displaystyle \frac{x^{2}+5}{x^{2}-4}=1+\frac{9}{x^{2}-4}$
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, $P(x)=x^{2}+5, \quad $is $2$, and
the degree of the denominator$ , Q(x)=x^{2}-4, \quad $is $2$.
The rational expression is improper.
To make it proper,
$\displaystyle \frac{x^{2}+5}{x^{2}-4}$=$\displaystyle \frac{x^{2}-4+4+5}{x^{2}-4}=\frac{x^{2}-4}{x^{2}-4}+\frac{9}{x^{2}-4}$
$=1+\displaystyle \frac{9}{x^{2}-4}$
