Emirhan wrote: For all $x \geq 2$, $y \geq 2$ real numbers, prove that $$x(\frac{4x}{y-1}+\frac{1}{2y+x})+y(\frac{y}{6x-9}+\frac{1}{2x+y}) > \frac{26}{3}$$ $\frac{x}{2y+x}+\frac{y}{2x+y}\geq \frac{2}{3}$ , $\frac{4x^2}{y-1}+\frac{y^2}{6x-9} \geq 8$