Question

Salutari! As vrea sa stiu cum se calculeaza elementeu neutru pentru o fractie, ca in aceasta lege.

Answer 1

$\it x*y=\dfrac{xy}{2xy-x-y+1}\\ \\ \\ x*e=x \Leftrightarrow \dfrac{xe}{2xe-x-e+1}=x|_{:x} \Leftrightarrow \dfrac{e}{2xe-x-e+1}=1 \Leftrightarrow\\ \\ \\ \Leftrightarrow 2xe-x-e+1=e \Leftrightarrow 2xe-x-e+1-e=0 \Leftrightarrow 2xe-2e-x+1=0 \Leftrightarrow \\ \\ \Leftrightarrow 2e(x-1)-(x-1) =0 \Leftrightarrow (x-1)(2e-1)=0 \Leftrightarrow 2e-1=0 \Leftrightarrow e=\dfrac{1}{2}$