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

Calculate the limit \( \lim_{x \rightarrow -5} \frac{x^{2}-25}{(x+5)(x-6)} \). Evaluate the limit by following steps: - step0: Evaluate using transformations: \(\lim _{x\rightarrow -5}\left(\frac{x^{2}-25}{\left(x+5\right)\left(x-6\right)}\right)\) - step1: Reduce the fraction: \(\lim _{x\rightarrow -5}\left(\frac{x-5}{x-6}\right)\) - step2: Rewrite the expression: \(\frac{\lim _{x\rightarrow -5}\left(x-5\right)}{\lim _{x\rightarrow -5}\left(x-6\right)}\) - step3: Evaluate: \(\frac{-10}{\lim _{x\rightarrow -5}\left(x-6\right)}\) - step4: Evaluate: \(\frac{-10}{-11}\) - step5: Reduce the fraction: \(\frac{10}{11}\) The limit of the expression \( \frac{x^{2}-25}{(x+5)(x-6)} \) as \( x \) approaches -5 is \( \frac{10}{11} \) or approximately 0.90909.