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Hello I have a quick algebra question.

If I have the following expression

$\large \frac{1}{x^2+1}$, and I multiply the numerator and the denominator by $(x^2+1)$.

Is there any way I can get $x^4+x^2−1$?

The reason I am asking this is because on a problem I did this expression came up and it confused I will post the link.

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    @akkkk If you check the edit history, you'll note that only formatting and grammatical changes were made. The original post was indeed unambiguous.2012-12-22

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Essentially repeating Tyler Bailey's comment, in the answer to the linked question you faced solving $x=\dfrac{1}{\sqrt{x^2+1}}.$

Squaring both sides, noting this might introduce spurious solutions, gave $x^2=\dfrac{1}{{x^2+1}}.$

Multiplying both sides by $x^2+1$ (not numerator and denominator), which might lead to spurious solutions of the form $x=\pm i$ but in fact does not here, gave $x^4 +x^2 =1.$

Subtracting $1$ from both sides gave $x^4 +x^2 -1 = 0.$

This is about changes to an equation not an expression.

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    Oh I see now gracias.2013-01-10