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Question
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`y (alpha/(alpha-x) + beta/(beta-x) + gamma/(gamma-x))`
`y/x (alpha/(1/(x-alpha)) + beta/(1/(x-beta)) + gamma/(1/(x-gamma)))`
`y (alpha/(1/(x-alpha)) + beta/(1/(x-beta)) + gamma/(1/(x-gamma)))`
`y/x ((alpha/x)/(1/(x-alpha)) + (beta/x)/(1/(x-beta)) + (gamma/x)/(1/(x-gamma)))`
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Solution
`y = (1/x)/(1/x - alpha) + (beta/x)/((1/x - alpha)(1/x - beta)) + (gamma/x^2)/((1/x - alpha)(1/x - beta)(1/x - gamma))`
`=(1/x^2)/((1/x - alpha)(1/x-beta)) + (gamma/x^2)/((1/x - alpha)(1/x-beta)(1/x - gamma))`
`y = (1/x^3)/((1/x - alpha)(1/x - beta))`
`=> log y = -3 log x (1/x - alpha) - log (1/x - beta) - log (1/x - gamma)`
`1/y dy/dx = (-3)/x - 1/(1/x - alpha) (-1/x - alpha) - 1/(1/x - beta) ((-1)/x^2) - 1/(1/x - gamma) (-1/x^2)`
`y = y/x [-3 + 1/x/1/x - alpha + 1/x/(1/x - beta) + 1/x/(1/x - gamma)]`
`y/x (alpha/(1/(x-alpha)) + beta/(1/(x-beta)) + gamma/(1/(x-gamma)))`
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