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Question
Given `(x^3 + 12x)/(6x^2 + 8) = (y^3+ 27y)/(9y^2 + 27)`. Using componendo and dividendo find x : y.
Solution
`(x^3 + 12x)/(6x^2 + 8) = (y^2 + 27y)/(9y^2 + 27)`
`=> (x^3 + 12x + 6x^2 + 8)/(x^3 + 12x - 6x^2 - 8) = (y^3 + 27y + 9y^2 + 27)/(y^3 + 27y - 9y^2 - 27` (Using componendo-dividendo)
`=> ((x + 2)^3)/(x - 2)^3 = ((y + 3)^3)/(y - 3)^3`
`=> ((x + 2)/(x - 2))^3 = ((y + 3)/(y - 3))^3`
`=> (x + 2)/(x - 2) = (y +3)/(y - 3)`
`=> (2x)/4 = (2y)/6` (Using componendo-dividendo)
`=> x/2 = y/3`
`=> x/y = 2/3 => x : y = 2 : 3`
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