Find the limit of $\frac{1+a^7}{1+a}$ as $a$ approaches $-1$

Find the limit

$\lim_{x\to1}\left(\frac{x^9-1}{x^5-1}\right)$

Find the limit

$\lim_{x\to2}\left(\frac{x^2-4x+4}{x^3-12x+16}\right)$

Find the limit

$\lim_{x\to1}\left(\frac{x^5-1}{x^3-1}\right)$

Find the limit

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

$factor\left(x^4+x^3-6x^2-4x+8\right)$

Find the limit

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

Find the limit

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