Question

Find the following limit.
$\underset{x\to -3}{lim}\frac{x^2-2x-15}{2x^2-x-21}.$

Answer 1

$\underset{x\to -3}{lim}\frac{x^2-2x-15}{2x^2-x-21}$ (By factorization method)

$=\underset{x\to -3}{lim}\frac{x^2-5x+3x-15}{2x^2-7x+6x-21}$

$=\underset{x\to -3}{lim}\frac{x(x-5)+3(x-5)}{2(2x-7)+3(2x-7)}$

$=\underset{x\to -3}{lim}\frac{(x+5)(x-5)}{(x+5)(2x-7)}$

$=\frac{-3-5}{-6-7}=\frac{-8}{-13}=\frac{8}{13}$.