How can we prove that $\left|\frac{x^2y^3}{x^4+y^4}\right|\leq |x|+|y|$?
I got this as homework but don't even know where to start. I've tried developing $(x+y)^4$ but that didn't help to find a connection.
How can we prove that $\left|\frac{x^2y^3}{x^4+y^4}\right|\leq |x|+|y|$?
I got this as homework but don't even know where to start. I've tried developing $(x+y)^4$ but that didn't help to find a connection.
If $x=0$ or $y=0$, then we got $0\leq 0$ else $|\frac{x^2y^3}{x^4+y^4}|\leq |\frac{x^2y^3}{2x^2y^2}|\leq \frac{1}{2}|y|\leq |x|+|y|$