Question

若a、b互为相反数,且ab≠0,则b除以a(a+1)+a除以b(b+1)的值是多少？?????

Answer 1

a b 为相反数 则 a+b=0 a= -b
b/a(a+1)= -a/a(a+1)= -1/a+1 a/b(b+1)= -b/b(b+1)=-1/b+1
b/a(a+1) + a/b(b+1)= (-1/a+1) + (-1/b+1) = -(b+1+a+1)/(a+1)(b+1)
=-2/(ab+a+ab+b) = -2/2ab = -1/ab

Answer 2

b÷[a(a+1)]+a÷[b(b+1)]
=-a÷[a(a+1)]-b÷[(b+1)]
=-1÷(a+1)-1÷(b+1)
=-1/a+1-1/1-a
=(通分)(a-1/1-a²)-(1+a/1-a²)
=a-1-1-a/1-a²
=-2/1-a²
=2/a²-1

Answer 3

a=-b
b/a(a+1)+a/b(b+1)=-a/a(a+1)-b/b(b+1)=-1/(a+1)-1/(b+1)=-1/(a+1)-1/(1-a)=(a+1-a+1)/(a²-1)=2/(a²-1)