Question

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

Answer 1

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