I am trying to solve this problem.
Let $\Delta$ be a positive number. I would like to find the values of $x$ and $y$ such that:
$$ \left(1+\dfrac{x}{1+y}\right)\cdot\left(1+\dfrac{y}{1+x}\right) \geqslant \Delta,\quad (P1) $$ where $x$ and $y$ are restricted to be non-negative numbers, i.e., $x>0$ and $y>0$.
How to express $(P1)$ in an equivalent form more simple? Like $(P1) \iff x \geqslant \Delta' \cdot y$.