Is $x=-1$ a Vertical tangent or Asymptote to the curve $f(x)=\frac{(x-1)^2}{x+1}$

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Is $x=-1$ a Vertical tangent or Asymptote to the curve $f(x)=\frac{(x-1)^2}{x+1}$

I have a little confusion about the difference between VT and Asymptote

we have

$$f'(x)=1-\frac{4}{(x+1)^2}$$ so

$$ \lim _{x \to -1^+} f'(x) \to - \infty$$ and

$$ \lim _{x \to -1^-} f'(x) \to - \infty$$ and

So at $x=-1$ $f(x)$ has VT.

Also by definition of asymptote we have

$$ \lim_{x \to -1^+} f(x) \to \infty$$ and

$$ \lim_{x \to -1^-} f(x) \to -\infty$$

hence $x=-1$ is Vertical Asymptote.

so is this correct?