inequalities

[triggg]

Hi there,

suppose that x/y>w/z

where all x,y,w,z are positive real numbers in (0,1).

Take two other real numbers 0<a<min(x,w) and 0<b<min(y,z).

Is it always the case that (x-a)/(y-b)>(w-a)/(z-b) ?

Thanks for your advice!

 

[pka]

suppose that x/y>w/z
where all x,y,w,z are positive real numbers in (0,1).
Take two other real numbers a<min(x,w) and b<min(y,z).
Is it always the case that (x-a)/(y-b)>(w-a)/(z-b) ?

Did you leave some information out?

Do we know that \(\displaystyle 0<a~\&~0<b~?\)

 

[triggg]

Did you leave some information out?

Do we know that \(\displaystyle 0<a~\&~0<b~?\)

Sure! Sorry I forgot to mention. I edited the post, thanks.

 

[Quaid]

At this help site, we like to see some initial effort. What have you considered or tried, so far? Thank you! :cool: