Question

x³-1/x³-6x+6/x
Factorise please​

Answer 1

$\huge\boxed{\fcolorbox{blue}{orange}{HELLO\:MATE}}$

GIVEN:

=$x^{3}-\dfrac{1}{x^{3}} -6x +\dfrac{6}{x}$

=$(x) ^{3}-(\dfrac{1}{x}) ^{3}-6x+\dfrac{6}{x}$

=$(x-\dfrac{1}{x}) (x^{2}+1+\dfrac{1}{x^{2}})-6x+\dfrac{6}{x}$

$\large\green{\boxed{a^{3}-b^{3}=(a-b) (a^{2}+b^{2}+ab}}$

=$(x-\dfrac{1}{x}) (x^{2}+1+\dfrac{1}{x^{2}})-6(x-\dfrac{1}{x})$

=$(x-\dfrac{1}{x})(x^{2}+1+\dfrac{1}{x^{2}}-6)$

=$(x-\dfrac{1}{x})(x^{2}+\dfrac{1}{x^{2}}-5)$

Answer 2

Answer:

=x^{3}-\dfrac{1}{x^{3}} -6x +\dfrac{6}{x}x

3

−

x

3

1

−6x+

x

6

=(x) ^{3}-(\dfrac{1}{x}) ^{3}-6x+\dfrac{6}{x}(x)

3

−(

x

1

)

3

−6x+

x

6

=(x-\dfrac{1}{x}) (x^{2}+1+\dfrac{1}{x^{2}})-6x+\dfrac{6}{x}(x−

x

1

)(x

2

+1+

x

2

1

)−6x+

x

6

\large\green{\boxed{a^{3}-b^{3}=(a-b) (a^{2}+b^{2}+ab}}

a

3

−b

3

=(a−b)(a

2

+b

2

+ab

=(x-\dfrac{1}{x}) (x^{2}+1+\dfrac{1}{x^{2}})-6(x-\dfrac{1}{x})(x−

x

1

)(x

2

+1+

x

2

1

)−6(x−

x

1

)

=(x-\dfrac{1}{x})(x^{2}+1+\dfrac{1}{x^{2}}-6)(x−

x

1

)(x

2

+1+

x

2

1

−6)

=(x-\dfrac{1}{x})(x^{2}+\dfrac{1}{x^{2}}-5)(x−

x

1

)(x

2

+

x

2

1

−5)