Let $r$ and $s$ be two strictly positive natural integers such that $r > s$. Justify that $$\frac { 1 } { ( r + k + 1 ) ( s + k + 1 ) } = \frac { 1 } { r - s } \left( \frac { 1 } { s + k + 1 } - \frac { 1 } { r + k + 1 } \right) .$$
Let $r$ and $s$ be two strictly positive natural integers such that $r > s$. Justify that
$$\frac { 1 } { ( r + k + 1 ) ( s + k + 1 ) } = \frac { 1 } { r - s } \left( \frac { 1 } { s + k + 1 } - \frac { 1 } { r + k + 1 } \right) .$$