Partial Fractions Question: $\frac1{s(n-s)}$

Question

How do you decompose the fraction

$$\frac1{s(n-s)} $$

to two fractions?

($s$ and $n$ are variables).

Answer 1

One may write, $$ \frac1{s(n-s)}=\frac1{n}\frac{n}{s(n-s)}=\frac1{n}\frac{(n-s)+s}{s(n-s)}=\frac1{n}\left(\frac1s+\frac1{n-s} \right)=\frac1{ns}+\frac1{n(n-s)}. $$