The examples in this subsection have been used for testing purposes by Matthias Goldgruber. Cancelling, again, can not be done by rewriting; see  Stefan Karnel's diploma thesis !

Multiply the terms, and cancel them as much as possible ...

No.1 3*(x+y) / (15*(x - y)) * 25*(x - y)^2 / (18*(x+y)^2) = ...

Actually, students in Austrian highschools are trained in doing such multiplications by hand !
No.2 CAUTION with this example left for further testing. See smltest/IsacKnowledge/rational.sml 'SRM.test'.

5*a * (a - b)^2 * (a + b)^3 / (7*b*(a - b)^3) * 7*b / (a + b)^3 = ...
No.3 x * y/(x*y - y^2) * (x^2 - x*y) = ...

This term simplifies most.
No.4 (4*x^2 + 4*x + 1) * ((x^2 - 2*x^3) / (4*x^2 + 2*x)) = ...
No.5 (x^2 - 2*x) / (x^2 - 3*x) * (x - 3)^2/(x^2 - 4) = ...