# What is the limit of (x^2 - 7x)/(x+1) as x goes to infinity?

I would say $\infty$:
${\lim}_{x \to \infty} \left(\frac{{x}^{2} - 7 x}{x + 1}\right) =$ collecting ${x}^{2}$ and $x$:
${\lim}_{x \to \infty} \left(\frac{{x}^{\cancel{2}} \left(1 - \frac{7}{x}\right)}{\cancel{x} \left(1 + \frac{1}{x}\right)}\right) =$
as $x \to \infty$ then $\frac{1}{x} ^ n \to 0$ so:
$\frac{\infty \left(1 - 0\right)}{1 + 0} = \infty$