$\lim_{x\to0}\:\frac{\left(4x^3+3x^2\right)}{\left(8x^3-14\right)}$

$\frac{\left(8z^3\:-y^6\:\right)}{2z\:-\:y^2}$

$\frac{x^5+x^3+\left(-1\right)x^2+3}{x^3+x^2+\left(-1\right)x+1}$

$\lim_{x\to4}\left(\frac{2-x}{2x-8}\right)$

$x^2-3x+6$

$\frac{\tan\left(x\right)-\cot\left(x\right)}{\tan\left(x\right)+\cot\left(x\right)}+1$

$\int8x^2\cdot\cos\left(6x\right)dx$