Factorize the following expression-x2-1-x2-2-3x-3-x

Factorizing the given expression:x^2+1/x^2 2 3x+3/x0ex0ex=x^2 2+1/x^2 3(x 1/x)0ex0ex=(x 1/x)^2 3(x 1/x) (Using the formula of (a b)^2=a^2 2ab+b^2)0ex0ex=(x ...

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Standard IX

Mathematics

Ratio and Proportion

Factorize the...

Question

Factorize the following expression:
$x^{2} + \frac{1}{x^{2}} - 2 - 3 x + \frac{3}{x}$

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Solution

Factorizing the given expression:
$x^{2} + \frac{1}{x^{2}} - 2 - 3 x + \frac{3}{x} = x^{2} - 2 + \frac{1}{x^{2}} - 3 (x - \frac{1}{x}) = {(x - \frac{1}{x})}^{2} - 3 (x - \frac{1}{x}) (U \sin g t h e f o r m u l a o f {(a - b)}^{2} = a^{2} - 2 a b + b^{2}) = (x - \frac{1}{x}) (x - \frac{1}{x} - 3)$
Hence, after factorizing we get $x^{2} + \frac{1}{x^{2}} - 2 - 3 x + \frac{3}{x} = (x - \frac{1}{x}) (x - \frac{1}{x} - 3) .$

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Factorize the following expression:x2+1x2-2-3x+3x

Factorizing the given expression:x2+1x2-2-3x+3x=x2-2+1x2-3(x-1x)=(x-1x)2-3(x-1x)(Usingtheformulaof(a-b)2=a2-2ab+b2)=(x-1x)(x-1x-3)Hence, after factorizing we get x2+1x2-2-3x+3x=(x-1x)(x-1x-3).

Factorize the following expression:
$x^{2} + \frac{1}{x^{2}} - 2 - 3 x + \frac{3}{x}$