Math doubt

Question

Is it true

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

Is it applied every function? (like limit func, generating func)?

Comments

I don't understand why are thinking like that, you may have got a few cases where it'd be working but in general,

$(1+x^2)^{-1}$ = $1 - x^2 + x^4 -x^6+...........$

and can't be approximated to just $1-x^2$

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yes thanks

and where it could be applied? I think limit func can never apply it

and generating function it will produce infinite series

So, can we conclude, it can never be applied?