(z^2-z-6)/(z-6)*(z^2-6z)/(z^2+2z-15)
color(white)("XXXX")Combining the numerator factors and the denominator factors:
=((z^2-z-6)(z^2-6z))/((z-6)(z^2+2z-15))
color(white)("XXXX")Factoring
= ((z-3)(z+2)(z)(z-6))/((z-6)(z+5)(z-3))
color(white)("XXXX")Cancelling out matching terms in the numerator and denominator
= (cancel((z-3))(z+2)(z)cancel((z-6)))/(cancel((z-6))(z+5)cancel((z-3)))
color(white)("XXXX")Rewrite simplified:
=(z^2+2z)/(z+5)