<s>[INST] Simplifying $\frac{x}{\sqrt[3]{x+1}-1}$ 
Simplify the following fraction:
$$\frac{x}{\sqrt[3]{x+1}-1}$$

How should I approach this? unlike $(a-b)(a+b)=a^2+b^2$?
 [/INST] Depending what you mean by simplify: presumably, get rid of the denominator.
Let $y = \sqrt[3]{x+1}$ then 
$$
\frac{x}{\sqrt[3]{x+1}-1} = \frac{y^3 -1}{y-1} = y^2 + y +1 = (x+1)^{\frac23} + \sqrt[3]{x+1} + 1
$$
</s>