Question

The value of $\underset{x\to -5}{lim}\frac{x^2-25}{x^2+2x-15}$ is

• A. $\frac{2}{3}$
• B. $\frac{-2}{3}$
• C. $\frac{5}{4}$
• D. $\frac{-5}{4}$

Answer 1

The correct option is C $\frac{5}{4}$

$\underset{x\to -5}{lim}\frac{x^2-25}{x^2+2x-15}$
This is $\frac{0}{0}$ form
$=\underset{x\to -5}{lim}\frac{(x-5)(x+5)}{(x-3)(x+5)}=\underset{x\to -5}{lim}\frac{x-5}{x-3}=\frac{-10}{-8}=\frac{5}{4}$