3) \( \lim _{x \rightarrow-5} \frac{x^{2}-25}{(x+5)(x-6)} \)

To find the limit \( \lim _{x \rightarrow-5} \frac{x^{2}-25}{(x+5)(x-6)} \), we first simplify the expression. Notice that \( x^2 - 25 \) can be factored as \( (x - 5)(x + 5) \). So we rewrite the limit: \[ = \lim_{x \rightarrow -5} \frac{(x - 5)(x + 5)}{(x+5)(x-6)} \] Now, we can cancel the \( (x + 5) \) terms from the numerator and denominator, since \( x \rightarrow -5 \) does not make \( x + 5 \) equal to zero in the context of the limit: \[ = \lim_{x \rightarrow -5} \frac{x - 5}{x - 6} \] Now, we can substitute \(-5\) into the simplified limit: \[ = \frac{-5 - 5}{-5 - 6} = \frac{-10}{-11} = \frac{10}{11} \] So, the limit is: \[ \lim _{x \rightarrow-5} \frac{x^{2}-25}{(x+5)(x-6)} = \frac{10}{11} \]