1
1)(a+b)/(a²-ab+b²)/(a+b)-ab=a²-ab+b²-ab=a²-2ab+b²=(a-b)²
2)(a-b)²:(a²-b²)=(a-b)²*1/[(a-b)(a+b)]=(a-b)/(a+b)
3)(a-b)/(a+b)+2b/(a+b)=(a-b+2b)/(a+b)=(a+b)/(a+b)=1
2
1)2+1/b=(2b+1)/b
2)(2b+1)/b : 2(4b²+4b+1)/[b(b-4)]*(2b+1)/[2(b-4)]=
=(2b+1)/b*b(b-4)/([2(2b+1)²]*(2b+1)/[2(b-4)]=1/4
3
1)(2a²-a-3)/(a²+5a+6):(2a-3)/(a-2)=((2a-3)(a+1)/[(a+2)(a+3)]*(a-2)/(2a-3)=
=(a+1)(a-2)/[(a+3)(a+2)]
2)(a+2)/(a-2)*(a+1)(a-2)/[(a+3)(a+2)]*(a+3)/(a+1)=1
4
1)3/(x-3)+4/[(x-3)(x-2)]+2x/(x-2)=(3x-6+4+2x²-6x)/[(x-3)(x-2)]=
=(2x²-3x-2)/[(x-3)(x-2)]=(2x+1)(x-2)/[(x-3)(x-2)]=(2x+1)/(x-3)
2)(2x+1)/(x-3):(2x+1)/3=(2x+1)/(x-3)*3/(2x+1)=3/(x-3)
3)3/(x-3)+(x-12)/[3(x-3)]=(9+x-12)/[3(x-3)]=(x-3)/[3(x-3)]=1/3