Finding a solutions for an equation

linear algebra – How to compute a extra frequent model of Vandermonde / Cauchy double alternant determinant retort

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linear algebra – How to compute a extra frequent model of Vandermonde / Cauchy double alternant determinant

assume some variables ${X_i}_{1le i le n}$, ${Y_i}_{1le i le n}$, and ${W_i}_{1le i le n}$. Does anybody know find out how to compute the next determinant?
$$
det ~ left(frac{W_j^{i-1}}{X_i+Y_j}capable)_{1le i,jle n}.
$$

Update: If you can too present an retort for the illustration the place $W_j=1$ for $jge2$, that will breathe sufficient for the issue I maintain encountered in my analysis.

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