Question

factorise:- x^2+1/x^2-2-3x+3/x​

Answer 1

answer:(x-{\frac{1}{x})(x-\frac{1}{x}-3)

Step-by-step explanation:

The given equation is:

x^2+{\frac{1}{x^2}}-2-3x+\frac{3}{x}x2+x21−2−3x+x3

Using the identity, (a-b)^2=a^2+b^2-2ab(a−b)2=a2+b2−2ab , we have

(x-\frac{1}{x})^2=x^2+{\frac{1}{x^2}-2

Thus, the given equation becomes,

x^2+{\frac{1}{x^2}}-2-3x+\frac{3}{x}=(x-\frac{1}{x})^2-3x+{\frac{3}{x}

=(x-\frac{1}{x})^2-3(x-{\frac{1}{x}})(x−x1)2−3(x−x1)

=(x-{\frac{1}{x})(x-\frac{1}{x}-3)

which is the required factorized form

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