Question

Se considera expresia E(x)=(x+1/2x+1)^-1 +(2/x+1 -1/x+2) : x^2+x-6/x^2-4 ,unde x e R\ {-2, -3, -1/2, -1, 2}. Aratati ca E(x)=2.

Answer 1

[tex]( \frac{x+1}{2x+1})^{-1}+(\frac{2}{x+1}-\frac{1}{x+2}):\frac{x^2+x-6}{x^2-4}=\\ \frac{2x+1}{x+1}+(\frac{2(x+2)}{(x+1)(x+2)}-\frac{x+1}{(x+2)(x+1)})*\\ \frac{x^2-4}{x^2+x-6}=\frac{2x+1}{x+1}+\frac{x+3}{(x+2)(x+1)}\frac{(x-2)(x+2)}{(x+3)(x-2)}=\\ =\frac{2x+1}{x+1}+\frac{1}{x+1}=\frac{2x+2}{x+1}=2[/tex]