Question

If x=√3+√2/√3-√2 and y=1,then x-y/x-3y is

Answer 1

x-y = [√3 + √2)]/√3 -√ 2) - 1

= [√3 + √2 - √3) + √2)]/ √3 - √2

= (2√2) / √3 -√2 .......(1)

x-3y = [√3 + √2]/√3 - √2 - 1*3

= [√3+ √2- 3{√3 + √2}]/ √3 - √2

= ( √3 + √2-3√3 + 3√2 ) / √3 - √2
= ( -2√3 + 4√2 ) /√3 - √2...........(2)


FROM (1) & (2)
x-y / x-3y = 2√2/ -2 ( √3- 2√2 ) { √3 - √2 cancelled}
= -√2/ √3 - 2√2

= -√2 / (√3 - 2√2)

or on rationalising ,

x-y / x-3y = -√2 { √3 + 2√2} / 3 - 4*2
= -(√2*√3 +2*2 ) / -5

= (√6 + 4)/5