Reduce a fraction by interpolation

Question

I am trying to solve this problem:

Use $ x^2+1$ (polynomial interpolation) to reduce $$ \frac{(x^2+1)}{x(x-1)(x-2)(x-3)}.$$

I don't know how I can reduce a fraction by interpolation method.

Answer 1

You are to compute a third degree Lagrange interpolation polynomial with the roots $x=0,1,2,3$ of the denominator as sample points. That way you obtain the partial fraction decomposition of this rational function in a systematic way.