If a + b + c = 3, then find the value of 1/(1 - a)(1 - b) + 1/(1 - b)(1 - c) + 1/(1 - c)(1 - a).

Given,

a + b + c = 3

Now,

[1/(1 – a)(1 – b)] + [1/(1 – b)(1 – c)] + [1/(1 – c)(1 – a)]

By taking the LCM of denominators, we get;

= [(1 – c) + (1 – a) + (1 – b)]/ [(1 – a)(1 – b)(1 – c)]

= [3 – (a + b + c)]/ [(1 – a)(1 – b)(1 – c)]

= (3 – 3)/ [(1 – a)(1 – b)(1 – c)] {from the given}

= 0

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