$x^2-12x+27=0$

$\lim_{x\to\infty}\left(\frac{x}{2x-1}\right)^{\frac{1}{\left(x-1\right)}}$

$\frac{9}{3x}\frac{4}{x+2}$

$\frac{\left(2x\sqrt{x}-\frac{x^2}{2\sqrt{x}}\right)}{x}$

$\frac{d}{dx}\:y=\frac{5x+1}{9x-2}$

$\frac{dy}{dx}+10y-100=0$

$\int4x.\log\left(x+1\right)dx$