<s>[INST] Simplifying $\frac{1}{x^3+y^3} + \frac{1}{x^6+y^6}$ Simplify: $$\frac{1}{x^3+y^3}  + \frac{1}{x^6+y^6}$$
I know $\frac {na}{nb} = \frac {a}{b}$.
But I also know $(\frac{a}{b})^2 =  \frac {a^2}{b^2} \neq \frac{a}{b}$
So how do I get the same denominator (go from $x^3+y^3$ to $x^6+y^6$) if I can't just square it, since that would change its value? And even if I did just square it, I would be left with an extra $2x^3y^3$, which is another problem I don't know how to handle. Any guidance on handling these type of problems would be appreciated thanks.
 [/INST] How about if you let $x^3 = a$ and $y^3 = b$?
Then $x^3 + y^3 = a + b$ and $x^6 + y^6 = a^2 + b^2$.
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