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Given, (a+b)²/ab+(b+c)²/bc+(c+a)²/ac
and, a+b+c = 0
So, a+b = -c , b+c = -a , a+c = -b
Substituiting the values into the expression
(-c)²/ab + (-a)²/bc + (-b)²/ac
= c³/abc + a³/abc + b³/abc
= a³+b³+c³/abc
As a+b+c = 0 , So a³+b³+c³ will be equal to 3abc
= 3abc/abc
= 3
Hope it helps.
Thanks!!!
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