variation

(a)
Given x²-y² = k(x² y²) ,where k is a non-zero constant
.......x²(1-k) = y²(1 k)
................x = (+/-) root[(1+ k)/(1-k)] y
................x = h y ,where h is also a non-zero constant
So, we have y varies direcyly as x

(b)
Let (1-k) = (1+ k)h ,where both h and k are non-zero conatants
.......... x = x
...(1-k) x = (1+ k)h x
.....x - kx = h (x+ kx)
From part (a), we can express y = kx
Put y = kx into the above result, we have x-y = h(x+ y)
So, we have (x-y) varies directly as (x+ y)


p.s. the method in part (b) is commonly used

this can make the proof easier as we respect the unique condition stated in the requirement