Salut.
[tex]\displaystyle{E(x)= (\frac{1}{x+2}+\frac{x^{2}+3x+2}{x^{2}+4x+4}-\frac{x}{x-2}):\frac{x+2}{x^{2}-4} }[/tex]
[tex]\displaystyle{E(x)=(\frac{1}{x+2}+\frac{x^{2}+2x+x+2}{(x+2)^{2}}-\frac{x}{x-2}):\frac{x+2}{x^{2}-4} }[/tex]
[tex]\displaystyle{E(x)=(\frac{1}{x+2}+\frac{x^{2}+2x+x+2}{(x+2)^{2}}-\frac{x}{x-2}):\frac{x+2}{x^{2}-4} }[/tex]
[tex]\displaystyle{E(x)=(\frac{1}{x+2}+\frac{(x+2) \times (x+1)}{(x+2)^{2}}-\frac{x}{x-2}):\frac{x+2}{x^{2}-4} }[/tex]
[tex]\displaystyle{E(x)=(\frac{1}{x+2}+\frac{x+1}{x+2}-\frac{x}{x-2}):\frac{x+2}{x^{2}-4} }[/tex]
[tex]\displaystyle{E(x)=\frac{x-2+(x-2) \times (x+1) - x \times (x + 2)}{(x+2) \times (x-2)}:\frac{x+2}{x^{2}-4} }[/tex]
[tex]\displaystyle{E(x)=\frac{x-2+x^{2}+x-2x-2-x^{2}-2x}{(x+2) \times (x-2)}:\frac{x+2}{x^{2}-4} }[/tex]
[tex]\displaystyle{E(x)=\frac{-4-2x}{(x+2)\times (x-2)} : \frac{x+2}{x^{2}-4} }[/tex]
[tex]\displaystyle{E(x)=\frac{-2(x + 2)}{(x+2) \times (x-2)} : \frac{x + 2}{x^{2}-4} }[/tex]
[tex]\displaystyle{E(x)=\frac{-2}{x-2}:\frac{x+2}{x^{2}-4} }[/tex]
[tex]\displaystyle{E(x)=-\frac{2}{x-2} \times \frac{x^{2}-4}{x+2} }[/tex]
[tex]\displaystyle{E(x)=-\frac{2}{x-2} \times \frac{(x-2) \times (x+2)}{x+2} }[/tex]
[tex]\boxed{E(x) = -2}[/tex]
Expresia dată este constantă, întrucât are aceeași valoare pentru orice [tex]\displaystyle{x}[/tex] ∈ R.
- Lumberjack25
