Answer
The rational expression is proper.
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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$P(x)=x, \quad Q(x)=x^{2}-1$
The degree of the numerator is $1$,
the degree of the denominator is $2$.
The rational expression is proper.