1)(a²-ax)/(a²x-ax²) - 1/x=a(a-x)/ax(a-x) - 1/x=1/x-1/x=0
2)(mn^4 -an^4)/(an³-mn³) + 2n=n^4(m-a)/n³(a-m) + 2n=-n+2n=n
3) (x²-1)/(1-x³)-x²/(x²+x+1)=(x-1)(x+1)/(1-x)(1+x+x²) - x²/(x²+x+1)=
=-(x+1)/(1+x+x²) - x²/(x²+x+1)=(-x-1-x²)/(x²+x+1)=-(x²+x+1)/(x²+x+1)=-1
4)a/(a²-3a)+(a-8)/a+(7a²-3a-72)/(a³-9a)=a/a(a-3) + (a-8)/a+(7a²-3a-72)/a(a-3)(a+3)=
=1/(a-3)+(a-8)/a+(7a²-3a-72)/a(a-3)(a+3)=(a²+3a+a³-9a-8a²+72+7a²-3a-72)/a(a²-9)=
=(a³-9a)/a(a²-9)=a(a²-9)/a(a²-9)=1
5)(1/a²+1/b²+2/(a+b)*(1/a+1/b))/((a+b)/ab)²=1
1/a+1/b=(a+b)/ab
2/(a+b)*(a+b)/ab=2/ab
1/a²+1/b²+2/ab=(b²+a²+2ab)/a²b²=(a+b)²/a²b²
((a+b)/ab)²=(a+b)²/a²b²
(a+b)²/a²b²: (a+b)²/a²b²=1