<s>[INST] Finding $\lim\limits _{x\to-\infty} \frac{\sqrt[3]{x^3+x}}{x}$ 
$$\lim\limits _{x\to-\infty} \frac{\sqrt[3]{x^3+x}}{x}$$

I have to resolve this limit, I tried factoring out x, I tried rewriting $x^3+x$ as 
$x^3(1+ \frac{x}{x^3})$ and it doesn't seem to cancel. What should I do?
 [/INST] $$\lim_{x\to-\infty} \frac{\sqrt[3]{x^3+x}}{x}=\lim_{x\to-\infty} \sqrt[3]{\frac{x^3+x}{x^3}} =\lim_{x\to-\infty} \sqrt[3]{1+\frac{1}{x^2}}  = \sqrt[3]{1+\lim_{x\to-\infty}\frac{1}{x^2}}=1$$
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