Question

`\lim_(x \to \-1) (x^(2) +x ) / (x-1)`

Answer 1

The limit does not exist, since the limit from the left is
`-\infty` while the limit from the right is
`+\infty`.

Or did you mean


`\displaystyle\lim_(x\to1)(x^2-x)/(x-1)\,?`

In that case, as
`x\\eq1`, we have


`(x^2-x)/(x-1)=(x(x-1))/(x-1)=x`

which would make the limit 1.