Solve the equation in real positive numbers

[kate]

Solve the equation in real positive numbers:
x²y²+ x² + y² = x²y + xy² + xy.

[MM]

Is this mine? I think it has a lot to do with this. However it's easy. We can solve it by solving quadratic equation about x or using the inequality [tex]\frac{ab}{c}+\frac{bc}{a}+\frac{ca}{b}\ge a+b+c[/tex] and replacing c with 1. Equality holds for x=y=1.