Answer
$-12$
Work Step by Step
$\lim _{x\rightarrow -1}\dfrac {\left( 2x-1\right) ^{2}-9}{x+1}=\dfrac {\left( 2x-1\right) ^{2}-3^{2}}{x+1}=\dfrac {\left( 2x-1+3\right) \left( 2x-1-3\right) }{x+1}=\dfrac {\left( 2x+2\right) \left( 2x-4\right) }{x+1}=\dfrac {2\left( x+1\right) \left( 2x-4\right) }{x+1}=2(2x-4)=4x-8=4\times (-1)-8=-12$
