8
1)a/b+b/a=(a²+b²)/ab
2)a/b +2 +b/a=(a²+2ab+b²)/ab=(a+b)²/ab
3)(a²+b²)/ab:(a+b)²/ab=(a²+b²)/ab*ab/(a+b)²=(a²+b²)/(a+b)²
4)(1/a+1/b)²=[(b+a)/ab]²=(b+a)²/a²b²
5)2/ab:(b+a)²/a²b²=2/ab*a²b²/(a+b)²=2ab/(a+b)²
6)(a²+b²)/(a+b)²+2ab/(a+b)²=(a²+b²+2ab)/(a+b)²=(a+b)²/(a+b)²=1
9
1)m- mn/(m+n)=(m²+mn-mn)/(m+n)=m²/(m+n)
2)(m-n)/(m+n)+(m²+n²)/(m+n)²=(m²-n²+m²+n²)/(m+n)²=2m²/(m+n)²
3)1/(m+n)-1/m+(n+2)/m(m+n)=(m-m-n+n+2)/m(m+n)=2/m(m+n)
4)m²/(m+n):2m²/(m+n)²=m²/(m+n)*(m+n)²/2m²=(m+n)/2
5)(m+n)/2*2/(m(m+n)=1/m
10
1)(n+1)/(n-1)+(n-1)/(n+1)-2n²/(n-1)(n+1)=(n²+2n+1+n²-2n+1-2n²)/(n-1)(n+1)=
=2/(n-1)(n+1)
2)2/(n-1)(n+1)*0,5(n²+2n+1)=2/(n-1)(n+1)*0,5(n+1)²=(n+1)/(n-1)