Answer = -4
Given the above function
[tex]\begin{gathered} \lim _{x\rightarrow-1}\frac{2x^2\text{ - 2}}{x\text{ + 1}} \\ 2x^2-2=2(x^2\text{ - 1)} \\ \lim _{x\rightarrow-1}\frac{2x^2-\text{ 2}}{x\text{ + 1}}\text{ = }\frac{2(x^2\text{ - 1)}}{x\text{ + 1}} \\ \lim _{x\rightarrow-1}\frac{2x^2\text{ - 2}}{x\text{ + 1}}\text{ = }\frac{2\lbrack(x\text{ - 1)(x + 1)\rbrack}}{x\text{ + 1}} \\ \lim _{x\text{ }\rightarrow-1}\frac{2x^2-2}{x\text{ +1}}\text{ = 2(x - 1)} \\ \text{Substitute the value of }x\text{ = -1 into the function} \\ 2(-1\text{ - 1)} \\ 2(-2)\text{ = -4} \\ \lim _{x\text{ }\rightarrow-1}\frac{2x^2\text{ - }2}{x+\text{ 1}}\text{ = -4} \end{gathered}[/tex]