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Se considera expresia E(x)= [tex] \frac{x+1}{ x^{2} +1 } : \frac{ (x-1)^{2} -x(x-2)}{ x^{2} +1 } [/tex] , unde x este numar real.
Rezolvati, in multimea numerelor reale, ecuatia E(x)=1


Răspuns :

[tex] \frac{x+1}{ x^{2}+1 } : \frac{ x^{2} -2x+1- x^{2} +2x}{ x^{2} +1} [/tex]=
[tex] \frac{x+1}{ x^{2} +1} * \frac{ x^{2} +1}{ x^{2} -2x+1- x^{2} +2x} = \frac{x+1}{1} =x+1 [/tex]