#### Answer

$\dfrac {4}{7}$

#### Work Step by Step

$\lim _{u\rightarrow 1}\dfrac {u^{4}-1}{u^{3}+5u^{2}-6u}=\dfrac {\left( u^{2}-1\right) \left( u^{2}+1\right) }{u\left( u^{2}+5u-6\right) }=\dfrac {\left( u-1\right) \left( u+1\right) \left( u^{2}+1\right) }{u\left( u-1\right) \left( u+6\right) }=\dfrac {\left( u+1\right) \left( u^{2}+1\right) }{u\left( u+6\right) }=\dfrac {4}{7}$