<s>[INST] Prove that $\left|\frac{x^3y^3}{9x^4+y^4}\right| \le \frac{x^2+y^2}{6}$ I need to prove that: $$\left|\frac{x^3y^3}{9x^4+y^4}\right| \le \frac{x^2+y^2}{6}$$
I am new to inequalities so I only tried C-S and  AM-GM but none of those work.
Any hints on how to proceed here?.
 [/INST] $(9x^4 + y^4)(x^2 + y^2)\ \ge\ (3x^3 + y^3)^2\ \ge\ |6x^3y^3|$
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