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in my calculus introduction book, it is written:

Let a rational function: [tex]f(x) = \frac{{p(x)}}{{q(x)}}[/tex] and a, a real number

If q(a) equals 0, but not p(a), then [tex]{\lim }\limits_{x \to a} f(x)[/tex] does not exist.

however, while doing exercises on the internet, i found that:

[tex]{\lim }\limits_{x \to 1} \frac{{2 - x}}{{(x - 1)^2 }} = \infty[/tex]

is my textbook wrong?

thank you