Question

Solve : $\underset{x\to 3}{It}\frac{x^2+2x-15}{x^2-9}$

Answer 1

$\underset{x\to 3}{Iim}\frac{x^2+2x-15}{x^2-9}$

$\Rightarrow \underset{x\to 3}{Iim}\frac{x^2+5x-3x-15}{(x+3)(x-3)}$

$\Rightarrow \underset{x\to 3}{Iim}\frac{x(x+5)-3(x+5)}{(x-3)(x+3)}$

$\Rightarrow \underset{x\to 3}{Iim}\frac{(x+5)(x-3)}{(x-3)(x-3))}$

$\Rightarrow \underset{x\to 3}{Iim}\left(\frac{x+5}{x+3}\right)$

$\Rightarrow \frac{3+5}{3+3}\Rightarrow \frac{8}{6}\Rightarrow \frac{4}{3}$

$\therefore \underset{x\to 3}{lim}(x^2+2x-15)(x^2-9)=\frac{3}{4}$