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If y=(ax^2)/((x-a)(x-b)(x-c))+(b x)/((x-...

If `y=(ax^2)/((x-a)(x-b)(x-c))+(b x)/((x-b)(x-c))+c/(x-c)+1`, then prove that `(y')/y=1/x[a/(a-x)+b/(b-x)+c/(c-x)]`

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To prove that \(\frac{y'}{y} = \frac{1}{x}\left[\frac{a}{a-x} + \frac{b}{b-x} + \frac{c}{c-x}\right]\) for the given function \[ y = \frac{ax^2}{(x-a)(x-b)(x-c)} + \frac{bx}{(x-b)(x-c)} + \frac{c}{(x-c)} + 1, \] we will follow these steps: ...
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