Let us evaluate $\lim _{x_{x}-2} \frac{3 x^{2}+x-10}{x+2}$

Ask yourself the following questions:

1. Is the function $f(x)$ a polynomial function?

Answer: No, but the numerator and denominator separately are polynomials. They are combined into a single mathematical formula and so are now a closed-form function.

2. Is the value $x=a$ in the domain of $f(x)$ ?

Answer: No, since $\left(3(-2)^{2}+(-2)-10\right) /((-2)+2)$ is not defined.

Therefore, we consult the above Question/Answer discussion, and simplify the function, if we can.

$\frac{3 x^{2}+x-10}{x+2}=\frac{(x+2)(3 x-5)}{(x+2)}=3 x-5$

Since we are now left with a polynomial function that is defined when $x=-2$, we can now evaluate the limit by substitution:

$\operatorname{Lim}_{x_{\rightarrow}-2} \frac{3 x^{2}+x-10}{x+2}=\lim _{x_{\rightarrow}-2} 3 x-5=3(-2)-5=-11$