Explain why $\underset{x3}{lim}\frac{x^{2}2x-15}{x-3}=\underset{x3}{lim}(x5),$ and then evaluate $\underset{x3}{lim}\frac{x^{2}2x-15}{x-3}$

Choose the correct answer below.

A$.$ Since $\frac{x^{2}2x-15}{x-3}=x5$ whenever $x3,$ it follows that the two expressions evaluate to the same number as $x$ approaches $3.$

B$.$ The limits $\underset{x3}{lim}\frac{x^{2}2x-15}{x-3}$ and $\underset{x3}{lim}(x5)$ equal the same number when evaluated using direct substitution.

C$.$ Since each limit approaches $3,$ it follows that the limits are equal.

D$.$ The numerator of the expression $\frac{x^{2}2x-15}{x-3}$ simplifies to $x5$ for all $x,$ so the limits are equal.