Question

Right answer will mark in brainlist and wrong answer will be reported.
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Factorise.
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Answer 1

Question:

Factorise : x² + 1/x² - 2 - 3x + 3/x

Answer:

( x - 1/x )( x - 1/x - 3 )

Step-by-step explanation:

x² + 1/x² - 2 - 3x + 3/x

It can be written as

= ( x )² + ( 1/x )² - 2( x )( 1/x ) - 3( x - 1/x )

Using algebraic identity a² + b² - 2ab = ( a - b )²

= ( x - 1/x )² - 3( x - 1/x )

Taking ( x - 1/x ) common

= ( x - 1/x )( x - 1/x - 3 )

Hence the expression is factorised.

Additional information :

Factorisation :

Expressing an expression or polynomial as its products is known as factorisation.

Factorisation can be done done using these methods

• Algebraic identities
• Splitting the middle term and so on

Some important algebraic identities :

• ( a + b )² = a² + b² + 2ab

• ( a - b )² = a² + b² - 2ab

• ( a + b )( a - b ) = a² - b²

• ( x + a )( x + b ) = x² + ( a + b )x + ab

Answer 2

Answer:

$x^2+\frac{1}{x^2} -2-3x+\frac{3}{x}\\\\ => x^2+\frac{1}{x^2}-2.x^2.\frac{1}{x^2}-3(x-\frac{1}{x} )\\\\ =>(x-\frac{1}{x} )^2-3(x-\frac{1}{x})\\\\=>(x-\frac{1}{x} )[(x-\frac{1}{x} )-3]\\\\=>(x-\frac{1}{x} )(x-\frac{1}{x}-3)$