Mathematico | Mathematico

The function $f$ is defined by

f (x) = \frac{k x}{(x + k)^{2}}, x \neq - k

Find, in terms of $k,$ expressions for $A$ and $B$ such that

f (x) = \frac{A}{x + k} + \frac{B}{(x + k)^{2}}

This is a bit like Exercise 3 where you have a repeated root. You will need to let $x = - k$ to find $B$ and then compare the coefficient of $x$ to find $A .$ Just treat $k$ as if it were any fixed number.