Question

Factorise 2+1/x²+2-2x-2/x​

Answer 1

Answer:

Given,

x

2

+

x

2

1

+2−2x−

x

2

=x^{2}+\frac{1}{x^{2}}+2\times x \times \frac{1}{x}-2x-\frac{2}{x}=x

2

+

x

2

1

+2×x×

x

1

−2x−

x

2

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

x

1

)

2

−2(x+

x

1

)

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

x

1

)(x+

x

1

−2)

Therefore,

\begin{gathered}x^{2}+\frac{1}{x^{2}}+2-2x-\frac{2}{x}\\=\big(x+\frac{1}{x}\big)\big(x+\frac{1}{x}-2\big)\end{gathered}

x

2

+

x

2

1

+2−2x−

x

2

=(x+

x

1

)(x+

x

1

−2)