If `a^(2), b^(2),c^(2) ` are in A.P prove that `(a)/(b+c), (b)/(c+a) ,(c)/(a+b)` are in A.P.

Explanation

` a^(2) , b^(2) , c^(2)` are in A.P.
Adding ` ab + bc + ca `
` rArr (a + b)(a + c), (b + c) (b + a), (c + a) (c + b)` are in A.P.
Divide by ` (a + b) (b + c)( (c + a)`
` rArr (1) /(b +c) , (1), (c + a) , (1)/(a +b)` are in A.P.
Multiply by ` a + b + c ` . and subtarct 1,
` (a)/(b + c) , (b)/(c +a), (c)/(a + b)` are in A.P.