$\begin{array}{l}\mathrm{simplify((x**3+x**2-x-1)/(x**2+2x+1))}\\ \mathrm{>>>}x-1\end{array}$

$\begin{array}{l}\mathrm{collect(x*y+x-3+2*(x**2)-z*(x**2)+x**3,x)}\\ \mathrm{>>>}{x}^3+x^2*(-z+2)+x*(y+1)-3\end{array}$

$\begin{array}{l}\mathrm{expand((x+1)**2)}\\ \mathrm{>>>}{x}^2+2*x+1\end{array}$

$\begin{array}{l}\mathrm{factor(x**3-x**2+x-1)}\\ \mathrm{>>>}(x-1)*(x^2+1)\end{array}$

$\begin{array}{l}\mathrm{ratsimp(1/x+1/y)}\\ \mathrm{>>>}\frac{x+y}{x*y}\end{array}$

$\begin{array}{l}\mathrm{lcm(9,6)}\\ \mathrm{>>>}18\end{array}$

$\begin{array}{l}\mathrm{lcm(x*(y**2)+(x**2)*y,(x**2)*(y**2))}\\ \mathrm{>>>}{x}^3*y^2+x^2*y^3\end{array}$

$\begin{array}{l}\mathrm{gcd(9,6)}\\ \mathrm{>>>}3\end{array}$

$\begin{array}{l}\mathrm{gcd(x*(y**2)+(x**2)*y,(x**2)*(y**2))}\\ \mathrm{>>>}x*y\end{array}$

$\begin{array}{l}\mathrm{subs(x+5,x,1)}\\ \mathrm{>>>}6\end{array}$