分式1/a+1/b=1/(a+b),那么a/b+b/a值为

Question

分式1/a+1/b=1/(a+b),那么a/b+b/a值为

Answer 1

1/a + 1/b=(a+b)/ab=1/(a+b)
(a+b)^2=ab
b/a + a/b=(a^2+b^2)/ab
=[(a+b)^2-2ab]/ab
=(a+b)^2/ab-2
=1-2
=-1