Question

evaluate the limit: $lim_{x
ightarrow - 3}\frac{7x + 21}{x^{2}+x - 6}$

Explanation:

Step1: Factor the numerator and denominator

Factor $x^{2}+x - 6=(x + 3)(x - 2)$ and $7x+21 = 7(x + 3)$. So the limit becomes $\lim_{x
ightarrow - 3}\frac{(x + 3)(x - 2)}{7(x + 3)}$.

Step2: Cancel out the common factor

Cancel out the common factor $(x + 3)$ (since $x
eq - 3$ when taking the limit), we get $\lim_{x
ightarrow - 3}\frac{x - 2}{7}$.

Step3: Substitute the value of $x$

Substitute $x=-3$ into $\frac{x - 2}{7}$, we have $\frac{-3-2}{7}=\frac{-5}{7}$.

Answer:

$-\frac{5}{7}$