1
1)1-1/(1-a)=(1-a-1)/(1-a)=a/(a-1)
2)(a-2a²)/(1-a)+a=(a-2a²+a-a²)/(1-a)=(2a-3a²)/(1-a)=(3a²-2a)/(a-1)
3)a/(a-1):(3a²-2a)/(a-1)=a/(a_1)*(a-1)/[a(3a-2)]=1/(3a-2)
2
1)(a-b)/a(a+b)-a/b*a+b)=(ab-a²-b²)/[ab(a=b)]
2)1/(a+b)+b²/[a(a-b)(a+b)]=(a²-ab+b²)/[a(a-b)(a+b)]
3)-(a²+ab+b²)/[ab(a+b)]:(a²-ab+b²)/[a(a-b)(a+b)]=
=-(a²-ab+b²)/[ab(a+b)]*a(a-b)(a+b)/(a²-ab+b²)=-(a-b)/b=(b-a)/b
3
1)(a-3)(a+3)/(a²-2a+4):(a+3)/[9(a+2)(a²-2a+4)]=
=(a-3)(a+3)/(a²-2a+4)*9(a+2)(a²-2a+4)/(a+3)=9(a+2)(a-3)
2)a²+9a+9(a+2)(a-3)=a²+9a+9a²+18a-27a-54=10a²-54
4
1)4a/[)a-1)(a+1)]+(a-1)/(a+1)=(4a+a²-2a+1)/[(a-1)(a+1)]=
=(a²+2a+1)/[(a-1)(a+1)]=(a+1)²/[(a-1)(a+1)]=(a+1)/(a-1)
2)(a+1)/(a-1)*2a/(a+1)=2a/(a-1)
3)2a/(a-1)-a/(a-1)-a/[(a-1)(a+1)]=a/(a-1)-a/[(a-1)(a+1)]=
=(a²+a-a)/(a²-1)=a²/(a²-1)