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Find the determinant

$$ \begin{vmatrix} \dfrac1{a_1+b_1} & \dfrac1{a_1+b_2} & \ldots & \dfrac1{a_1+b_n} \\ \dfrac1{a_2+b_1} & \dfrac1{a_2+b_2} & \ldots & \dfrac1{a_2+b_n} \\ \vdots & \vdots & \ddots & \vdots \\ \dfrac1{a_n+b_1} & \dfrac1{a_n+b_2} & \ldots & \dfrac1{a_n+b_n} \end{vmatrix} $$

I know you have to multiply -1 to the first row and add it to every rest rows, but I'm unsure of what to do after.

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    $\begingroup$ look up the cauchy/hilbert matrix $\endgroup$ – abel Jun 8 '15 at 3:57

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