; Some simplification tests Mathomatic has always been able to do.

clear all
2*(x^2 - y^2)^6 - (x^2 - y^2)^5*(2 x^2 - 3)
simplify
a^3/((a-b)*(a-c)) + b^3/((b-c)*(b-a)) + c^3/((c-a)*(c-b))
simplify
(x^6+a^6)*(x+1)/((x^6+a^6)*(x^2-a^2)+a^2*x^2*(x^4-a^4))+a^2*x^2*(x+1)/(x^6-a^6-a^2*x^2*(x^2-a^2))
simplify
((a*n + b*m)^2 + (a*m - b*n)^2) / ((a*p + b*q)^2 + (a*q - b*p)^2)
simplify
((p*x^2+(k-s)*x+r)^2-(p*x^2+(k+s)*x+r)^2)/((p*x^2+(k+t)*x+r)^2-(p*x^2+(k-t)*x+r)^2)
simplify
(1 - (1-(y+1)/(x+y+1)) / (1-x/(x+y+1))) / ((y+1)^2 - x / (1+x/(y-x+1))*(x*(y+1)/(y-x+1) - x))
simplify ; Any complex fraction can be reduced to a simple fraction.
((2*((x*(x + (((x^2) - 1)^(1/2)))) - 1)) + 1)/((2*x*((x^2) - 1)) + ((((x^2) - 1)^(1/2))*((2*(x^2)) - 1)))
simplify ; A good simplification resulting from trying to rationalize the denominator.