1)(x-√xy+y)/(√x-√y)=(x-√xy+y)(√x+√y)/x-y)=(x√x-x√y+y√x+x√y-y√x+y√y)/(x-y)=
=(x√x+y√y)/(x-y)=(√x³+√y³)/(x-y);
2)(9+3√a+a)/(3+√a)=(9+3√a+a)(3-√a)/(9-a)=(27+9√a+3a-9√a-3a-a√a)/(9-a)=
=(27-a√a)/(9-a)=(3³-√a³)/(9-a);
5)(√x-√y)/√y=(√xy-y)/y;
6)(a+√b)/a√b=(a+√b)·√b/ab=(a√b+b)/ab;
4)(a²b+2a√b+4)/(a√b+2)=(a²b+2a√b+4)(a√b-2)/(a²b-4)=
=(a³b√b+2a²b+4a√b-2a²b-4a√b-8)/(a²b-4)=(a³√b³-8)/(a²b-4);
3)(1-2√x+4x)/(1-2√x)=(1-2√x+4x)(1+2√x)/(1-4x)=
=(1-2√x+4x+2√x-4x+8x√x)/(1-4x)=(1+8√x³)/(1-4x)