$\frac{x+5}{-3}=3x-5$

$\left(5^2\right)^{-3}=5^{-6}$

$\int\left(\frac{y^2+y+1}{\sqrt{y}}\right)dy$

$\frac{\cos\left(a\right)-\sin\left(a\right)}{\cos\left(a\right)+\sin\left(a\right)}=\frac{\cos\left(2a\right)}{1+\sin\left(2a\right)}$

$9a^2b^2+30a^2bc+25a^2c^2$

$\frac{dy}{dx}=\frac{-2xy-1}{x^2}$

$-\frac{2}{\sqrt{x}}+\frac{5\sqrt{x}}{3}$