5
1)1/((a+b)+1/(a-b)+(a-b)/(a+b)²=((a+b)(a-b)+(a+b)²+(a-b)²)/(a+b)²(a-b)=
=(a²-b²+a²+2ab+b²+a²-2ab+b²)/(a+b)²(a-b)=(3a²+b²)/(a+b)²(a-b)
2)a-b²/a=(a²-b²)/a
3)(3a²+b²)/(a²-b²)(a+b) *(a²-b²)/a=(3a²+b²)/a(a+b)
6
1)1/(x+1)+3/(x(x+1)=(x+3)/x(x+1)
2)(x+5)/x(x+1)-+(x-1)/x(x+2)-1/x=
=[(x+2)(x+5)+(x+1)(x-1)-(x+1)(x+1)]/x(x+1)(x+2)=
=(x²+7x+10+x²-1-x²-7x-10)/x(x+1)(x+2)=
=(x²-1)/x(x+1)(x+2)=(x-1)(x+1)/x(x+1)(x+2)=(x-1)/x(x+2)
3)(x+3)/x(x+1)*x(x+2)/(x-1)=(x+3)(x+2)/(x²-1)
7
1)(5x+5)/(x²-x+1)-2/(x+1)=(5x²+5x+5x+5-2x²+2x-2)/(x³+1)=
=(3x²+12x+3)/(x³+1)
2)1+5/(x²-x+1)=(x²-x+1+5x)/(x²-x+1)=(x²+4x+1)/(x³-x+1)
3)3(x²+4x+1)/(x+1)(x²-x+1)*(x²-x+1)/(x²+4x+1)=3/(x+1)