It seems like a simple thing, but I am stucked on that for some time and decided ask for help...!
I see on a work that
\begin{align}&\dfrac{x-x^*}{x}(a-bxy-ax)+\dfrac{y-y^*}{y}(bxy-(a+c)y)\\&=b(x-x^*)(y-y^*)-a\dfrac{(x-x^*)^2}{xx^*}-b(x-x^*)(y-y^*)\\ &=-a\dfrac{(x-x^*)^2}{xx^*}\end{align}
where $a=-by^*+\dfrac{a}{x^*}$ and $a+c=bx^*$.
The cases I tried worked, but I'm definitely not getting algebraic development. Since now, grateful.
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Please, see Blue's comment for a simplification (which I unfortunately didn't manage to continue until the end).