limits - Find $lim_{xto -infty} frac{(x-1)^2}{x+1}$

Find $\lim_{x\to -\infty} \frac{(x-1)^2}{x+1}$

If I divide whole expression by maximum power i.e. $x^2$ I get,

$$\lim_{x\to -\infty} \frac{(1-\frac1x)^2}{\frac1x+\frac{1}{x^2}}$$

Numerator tends to $1$ ,Denominator tends to $0$

So I get the answer as $+\infty$

But when I plot the graph it tends to $-\infty$

What am I missing here? "Can someone give me the precise steps that I should write in such a case." Thank you very much!

NOTE: I cannot use L'hopital for finding this limit.

Answer

Hint: Write

$$\frac{x^2\left(1-\frac{1}{x}\right)^2}{x\left(1+\frac{1}{x}\right)}$$