$\lim_{n\to\infty}\:\frac{4^n}{1^n+1}$

$\frac{9x^2+5}{3x}$

$3\:\frac{3}{5}\cdot5$

$8x-5\left(x+6\right)-8$

$\lim_{x\to0}\left(\frac{9x\left(cos\left(2x\right)\right)-1}{sin\left(9x\right)-9x}\right)$

$\frac{a^4+2}{a^3}$

$\frac{\tan\left(x\right)}{\cot\left(x\right)}-\frac{\cot\left(x\right)}{\tan\left(x\right)}$