4
1)3/(x²-x+1)+1/(x+1)-3/(x+1)(x²-x+1)=(3x+3+x²-x+1-3)/(x+1)(x²-x=1)=
=(x²+2x+1)/(x+1)(x²-x+1)=(x+1)²/(x+1)(x²-x+1)=(x+1)/(x²-x+1)
2)x-(2x-1)/(x+1)=(x²+x-2x+1)/(x+1)=(x²-x+1)/(x+1)
3)(x+1)/(x²-x+1)*(x²-x+1)/(x+1)=1
5
1)(x-3)/(x²-3x+9)-(xy-3y)/(x+3)(x²-3x+9)=(x²-9-xy+3y)/(x³+27)=
=[(x+3)(x-3)-y(x-3)]/(x³+27)=(x-3)(x+3-y)/(x³+27)
2)(x-3)(x+3-y)/(x³+27)*y(x³+27)/(x-y+3)=y(x-3)