for all quadruples of positive real numbers w,x,z,y if w/x < y/z , then w/x < ( w+y / x+z ) and ( w+y / x+z ) < y/z.

I notice this is a false statement , provided by counter-example such as

m = 1 , x = 2 , y = 4 , z = 2

1/2 < 4/2 , 1/2 < 5/2 < 4/2 , however ,i try to disprove this statement algebraically using the negation of the statement.

exists quadruples of positive real number w , x, y , z , w/x < y/z and (w/x >= ( w+y / x+z ) or ( w+y / x+z ) >= y/z) something like this?.