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Question
Factorise `x^2 + 1/x^2 + 2 - 3x - 3/x`.
Solution
We have, `x^2 + 1/x^2 + 2 - 3x - 3/x`
= `x^2 + 1/x^2 + 2 * x * 1/x - 3(x + 1/x)`
= `(x + 1/x)^2 - 3(x + 1/x)` ...[Using the identity, a2 + b2 + 2ab = (a + b)2]
= `(x + 1/x)(x + 1/x - 3)` ...`["Taking" (x + 1/x) "as common"]`
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