<s>[INST] Factoring limits Couldn't find this limit someone help me? 
$$\lim_{x\rightarrow0} \frac{  (1+x)^{1/3} - (1-x)^{1/3}}{x}$$ 
I tried to take $x^{1/3}$ common from above expression
 [/INST] Let $A=(1+x)^{1/3}$ and $B=(1-x)^{1/3}$ then 
$$2x=A^3-B^3=(A-B)(A^2+AB+B^2)$$
Hence, as $x\to 0$, we have that $A\to 1$, $B\to 1$ and
$$\frac{\sqrt[3]{1+x}-\sqrt[3]{1-x}}x=\frac{A-B}{x}=\frac{2}{A^2+AB+B^2}\to\frac{2}{3}.$$
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