$\frac{x^3+27a^3}{x+3a}$

$\int-38df$

$\frac{\frac{7x^{2}}{9}}{\frac{6x^{4}}{5}}$

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

$\frac{d^2y}{dx^2}\left(\frac{1}{2}x-\frac{2}{5}x^{-4}-x^3-\frac{1}{15}\right)$

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

$\frac{2\sin\left(x\right)}{\cos\left(x\right)+\sin\left(x\right)}$