# What is  lim_(x->-oo) x^2/(x^2-7) ?

$1$
We can divide both numerator and denominator by ${x}^{2} :$
${\lim}_{x \to - \infty} \frac{\frac{\cancel{{x}^{2}}}{\cancel{{x}^{2}}}}{\frac{\cancel{{x}^{2}}}{\cancel{{x}^{2}}} - \frac{7}{x} ^ 2}$
$= {\lim}_{x \to - \infty} \frac{1}{1 - \frac{7}{x} ^ 2} = \frac{1}{1 - \frac{7}{- \infty} ^ 2} = 1$