Evaluate the limit lim x -> -1^+ (x^2 + x)/x^2 - 2x -3

If we get the 0/0 result while substituting the value then firstly we should look at whether we can factorize the given expression and then cancel the common terms and try not to get a 0/0 result. If we still get a 0/0 result, mark the answer as 'doesn't exist and move on.

In this question, you're right that we get 0/0 while substituting the value, BUT we can factorize the expressions and cancel the common terms. Let's do that!

= $\lim_{x \, \to \, -1^+}\frac{x^2 \, + \, x}{x^2 \, - \, 2x \, - 3}$

= $\lim_{x \, \to \, -1^+}\frac{x(x \, + \,1)}{(x \, - \, 3)(x \, + \, 1)}$

= $\lim_{x \, \to \, -1^+}\frac{x}{x \, - \, 3}$

Now, if we substitute the value of x = -1, we get $\frac 14$ and it is our final answer.

Positive sign in -1⁺ indicates that the value of x approaches -1 from the right side. That is -0.99, -0.999, -0.9999, ...

It is useful when we get a number/0 result and we need to find if it is -∞ or ∞ as done in this question.