$\frac{4x}{\left(x+2\right)\left(3x+2\right)}$

$11cos^2x+cosx-12$

$\frac{3x^4+5x\:-18}{x+1}$

$\frac{\cos x-\sin x-\cos^3x}{\cos\left(x\right)}=\sin^2x-\tan x$

$\frac{w^2+6w}{5w-30}\cdot\frac{w^2-36}{w^2+12w+36}$

$\int\frac{1}{x\left(3x+1\right)}dx$

$\frac{dy}{dx}=\frac{7+x+y}{1+x+y}$