$\frac{\left(x+7\right)}{2x^2-11x-6}$

$\lim_{x\to\infty}\left(\frac{2x^3+4x+9}{x^3+3x+16}\right)$

$x\frac{dy}{dx}=\frac{1}{y}$

$\frac{x^2+8x+1}{\left(x+1\right)^2}$

$\frac{dy}{dx}=x+5$

$\frac{\left(6x^3\:-\:2x^2+\:3\right)}{\left(x\:-\:2\right)}$

$-xsen\left(\frac{\pi}{6}\right)$