$\lim_{x\to0}\left(\frac{ln2x}{x-1}\right)$

$\lim_{n\to\infty}\left(\frac{n\left(n+1\right)}{\left(n+2\right)\left(n+3\right)}\right)$

$-6\left(3x\:-\:7\right)$

$\frac{x^3+2x+1}{x^2-x+3}$

$\lim_{x\to0}\left(\frac{\left(e^{9t}-1\right)}{\sin\left(t\right)}\right)$

$-6m+3t+4-4m-2t$

$\left(n+5\right)^3$