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If x = 3+ (3)/(y) + (3)/(y^(2)) + (3)/(y...

If `x = 3+ (3)/(y) + (3)/(y^(2)) + (3)/(y^(3)) + … + oo`, then `y`= ________.

A

`(x)/(3)`

B

`(x)/(x-3)`

C

`(1-x)/(3)`

D

`1-(3)/(x)`

Text Solution

Verified by Experts

The correct Answer is:
B
`x = 3 + (3)/(y) + (3)/(y^(2)) + (3)/(y^(3)) + ... + oo`
`x = 3 [(1)/(1-(1)/(y))]`
`x = 3 [(y)/(y-1)] rArr xy -x = 3y`
`xy - 3y = x`
`y (x-3) = x rArr y = (x)/(x-3)`.
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