$\lim\limits_{x\to -\infty} \quad \dfrac{x^4+x-1}{1-x^4}$
$=\lim\limits_{x\to -\infty} \quad \dfrac{x^4\bigg(1+\dfrac1{x^3}-\dfrac1{x^4}\bigg)}{x^4\bigg(\dfrac1{x^4}-1\bigg)}$
$=\lim\limits_{x\to -\infty} \quad \dfrac{1+\dfrac1{x^3}-\dfrac1{x^4}}{\dfrac1{x^4}-1}$
$=\dfrac{1+0-0}{0-1}=-1$
