Lagrange interpolating polynomial

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How can one find $$ L[x_0,x_1,..,x_n;\frac{1}{x+a}]?$$ The original problem asks for $$ L[x_0,x_1,..,x_n;\frac{x^{n+1}}{x\pm 1}]$$ I know there is a formula for $[x_0,x_1,..,x_n,\frac{f(x)}{a-x}]$, but I suppose it does not help.