Answer
$-3$
Work Step by Step
$\lim _{w\rightarrow -k}\dfrac {w^{2}+5kw+4k^{2}}{w^{2}+kw}=\dfrac {w^{2}+kw+4k^{2}+4kw}{w\left( w+k\right) }=\dfrac {w\left( w+k\right) +4k\left( w+k\right) }{w\left( w+k\right) }==\dfrac {\left( w+k\right) \left( w+4k\right) }{w\left( \omega +k\right) }=\dfrac {w+4k}{w}=\dfrac {-k+4k}{-k}=-3 $
