If a + b + c = 0 then the value of \frac{1}{(a+b)(b+c)}+ \frac{1}{(b+c)(c+a)} + \frac{1}{(c+a)(a+b)} is

SSC CGL Tier II 1 Dec 2016 Paper 1

Question : 67 of 100

Marks: +1, -0

a + b + c = 0

then the value of

{1}/{(a+b)(b+c)}+ {1}/{(b+c)(c+a)}

+ {1}/{(c+a)(a+b)}

Solution:

(1)

{1}/{(a+b)(b+c)}+ {1}/{(b+c)(c+a)}

+ {1}/{(c+a)(a+b)}

= {c+a+a+b+b+c}/{(a+b)(b+c)(c+a)}

= {2(a+b+c)}/{(a+b)(b+c)(c+a)}=0

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