Bonjour
Kimobu
[tex]x<y\ et\ 1+y>0\Longrightarrow\boxed{\dfrac{x}{1+y}<\dfrac{y}{1+y}}\\\\0<x<y\Longrightarrow1+x<1+y\\\\\Longrightarrow\dfrac{1}{1+x}>\dfrac{1}{1+y}\\\\\Longrightarrow\dfrac{y}{1+x}>\dfrac{y}{1+y}\\\\soit\ \ \boxed{\dfrac{y}{1+y}<\dfrac{y}{1+x}}[/tex]
d'où
[tex]\dfrac{x}{1+y}<\dfrac{y}{1+y}}<\dfrac{y}{1+x}}\Longrightarrow\boxed{\dfrac{x}{1+y}<\dfrac{y}{1+x}}}[/tex]
