A5. The rational function $f(x)=\frac{x^{2}-9}{x-1}$ has

(A) two poles and one zero.

(B) an oblique asymptote $y=x+1$ and a pole at the point $x=1$.

(C) a double zero at $x_{1,2}=3$.

(D) a graph that does not intersect the y-axis.

(E) no real zeros and a pole at the point $x=1$.
A5. The rational function $f(x)=\frac{x^{2}-9}{x-1}$ has one pole at $x=1$, zeros at $x=3$ and $x=-3$. It intersects the y-axis at $x=0$. Since $\frac{x^{2}-9}{x-1}=\frac{x^{2}-1-8}{x-1}=x+1-\frac{8}{x-1}$, $y=x+1$ is the oblique asymptote. The correct answer is (B).