adding 1 ,b+c-a /a + 1 ,c+a-b /b +1 , a+b-c/c + 1 =b+c/a ,c+a/b ,a+b/c.
adding 1 again, we get a+b+c/a ,a+b+c/b ,a+b+c/c
cancelling the numerator we get 1/a,1/b,1/c which are thus also in A.P.

-10

Asutosh Rath answered this

b+c-a/a, c+a-b/b, a+b-c/c in AP

ac-bc = ab-ac
/abc
1/b -1/a = 1/c-1/b
Hence they are in AP