$\frac{w_k}{x-x_k}$ expansion into decreasing powers of $x$

Question

How can $\dfrac {(w_k)}{(x-x_k)}$ becomes:$$\dfrac {w_k}x+\dfrac {w_kx_k}{x^2}+\dfrac {w_kx_k^2}{x^3}+...$$ I couldnt figured out the process.

Answer 1

Hint:

You can use this: $$\dfrac 1 {1-x}=\sum_{n=0}^\infty x^n$$ For $|x| <1$ and note that you have: $$\dfrac {w_k}{(x-x_k)}=\dfrac {w_k}{x}\dfrac {1}{(1-x_k/x)}$$