Question

x²+1/x²+1 factories​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Answer:     $x^2+\dfrac{1}{x^2}+1=\left(x+\dfrac{1}{x}+1\right)\left(x+\dfrac{1}{x}-1\right)$

Step-by-step explanation:

First you can notice that

$\left(x+\dfrac{1}{x}\right)^2=x^2+2x\cdot\dfrac{1}{x}+\left(\dfrac{1}{x}\right)^2=x^2+\dfrac{1}{x^2}+2$

so

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

then, applying that $a^2-b^2=(a+b)(a-b)$ we get

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