ReplaceAll[{(y[x]-y[x1])/(x-x1)==(y[x1]-y[x2])/(x1-x2)},{y[x_]->x^2+k/x}]ReplaceAll[{(y[x]-y[x1])/(x-x1)==(y[x1]-y[x2])/(x1-x2)},{y[x_]->x^2+k/x}]

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