\(\displaystyle{x}^{{-{{2}}}}\) is highest power of x in denominator. Dividing with \(x^{-2}\) is same as multiplying numerator and denominator with \(\displaystyle{x}^{{2}}\).

\(\lim_{x \to \infty} \frac{(x^{-1})+(x^{-4}))}{((x^{-2})−(x^{-3}))} \cdot \frac{(x^2)}{(x^2)}=\lim_{x \to \infty} \frac{(x+x^{-2})}{(1-x^{-1})}=\)

Use that \(\lim_{x \to \infty} x^{-n}=0 = \frac{(\infty+0)}{(1-0)}=\infty\)