factorise x^2 + 1/x^2+2 - 2x -2/x
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Answer:
( x + 1/x)( x + 1/x - 2)
Step-by-step explanation:
x^2 + 1/x^2 + 2 - 2x -2/x
= ( x + 1/x )^2 -2( x + 1/x ) since x^2 + 1/x^2 + 2 is in the form a^2 + b^2 + 2ab = ( a + b)^2
= ( x + 1/x )( x + 1/x - 2 )
Factorisation done here is by :
=> algebric identity a^2 + b^2 + 2ab = ( a + b) ^2
=> taking out the common term which is x + 1/x
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