Question

evaluate the limit, if it exists. (if an answer does not exist, enter dne.)
lim_{x
ightarrow - 5}\frac{x^{2}+5x}{x^{2}-3x - 40}

Explanation:

Step1: Factor the numerator and denominator

The numerator $x^{2}+5x=x(x + 5)$. The denominator $x^{2}-3x - 40=(x-8)(x + 5)$. So the function becomes $\frac{x(x + 5)}{(x - 8)(x+5)}$.

Step2: Simplify the function

Cancel out the common factor $(x + 5)$ (since $x
eq - 5$ when taking the limit), we get $\lim_{x
ightarrow - 5}\frac{x}{x - 8}$.

Step3: Substitute $x=-5$ into the simplified - function

Substitute $x=-5$ into $\frac{x}{x - 8}$, we have $\frac{-5}{-5-8}=\frac{-5}{-13}=\frac{5}{13}$.

Answer:

$\frac{5}{13}$