Evaluate each limit. 
lim x→−1 (x^2−4+ 3√x^2−9)

Verified step by step guidance

1. Step 1: Identify the form of the limit as x approaches -1. Substitute x = -1 into the expression x^2 - 4 + 3\sqrt{x^2 - 9} to check if it results in an indeterminate form.
2. Step 2: Simplify the expression. Notice that x^2 - 4 is a polynomial and 3\sqrt{x^2 - 9} is a radical expression. Simplify each part separately.
3. Step 3: Substitute x = -1 into the simplified expression. Calculate x^2 - 4 and 3\sqrt{x^2 - 9} separately to see if the limit can be directly evaluated.
4. Step 4: If direct substitution results in an indeterminate form, consider using algebraic manipulation or L'Hôpital's Rule if applicable. Check if the expression can be factored or simplified further.
5. Step 5: Evaluate the limit using the simplified expression or the result from L'Hôpital's Rule. Ensure that the final expression is not indeterminate and provides a clear value for the limit.