Question

如果a分之1+b分之1=a+b分之1，则a分之b+b分之a=

Answer 1

1/a+1/b=1/(a+b)
(a+b)/ab=1/(a+b)
∴(a+b)²/ab=1

a分之b+b分之a=
=(a²+b²)/ab
=[(a+b)²-2ab]/ab
=(a+b)²/ab-2ab/ab
=1-2
=-1

Answer 2

a分之1+b分之1=a+b分之1
两边同×(a+b)
1+b/a+1+a/b=1
b/a+a/b=-1