Find the limit of $\frac{x^2+6x+9}{x^2+7x+12}$ as $x$ approaches $-3$

Find the limit

$\lim_{x\to1}\left(\frac{2x^3-3x^2+1}{x^3-3x+2}\right)$

Find the limit

$\lim_{x\to-3}\left(\frac{x^4-81}{x+3}\right)$

Find the limit

$\lim_{x\to-1}\left(\frac{12x^3+12x^2}{x^4-x^2}\right)$

Find the limit

$\lim_{x\to1}\left(\frac{x^3-1}{4x^3-x-3}\right)$

Find the limit

$\lim_{x\to8}\left(\frac{x-8}{x^2-64}\right)$

Find the limit

$\lim_{x\to3}\left(\frac{x^3-27}{x^2-9}\right)$

Find the limit

$\lim_{x\to4}\left(\frac{2-\sqrt{x}}{4-x}\right)$