1) a(a-x)/ax(a-x)=1/x
2) n^4(m-c)/n^3(c-m)=n(m-c)/(c-m)=-n
3) (4p^2-16p^3)/(12p^2-3p)=(4p^2(1-4p))/(3p(4p-1))=-4p/3
4) (a^2-2a+1)/(a^2-1)=((a-1)^2)/((a-1)(a+1))=a-1/a+1
5) (b^3+1)/(b^2-b+1)=(b+1)(b^2-b+1)/(b^2-b+a)=b+1
6) (1-n^2)/(1-n^3)=(1-n)(1+n)/(1-n)(1+n+n^2)=1+n/1+n+n^2