[tex]\displaystyle\\
E(x)=\frac{x^2-x-2}{x^2-4}+\frac{x+1}{x+2}\\\\
\text{Aducem expresia la o forma mai simpla.}\\
\text{Descompunem in factori numaratorul si numitorul primei fractii.}\\
x^2-x-2=x^2-x-x+x-2=\\
=x^2-2x+x-2=x(x-2)+(x-2)=\boxed{\bf(x-2)(x+1)}\\\\
x^2-4 = \boxed{\bf(x+2)(x-2)}\\\\
E(x) =\frac{x^2-x-2}{x^2-4}+\frac{x+1}{x+2}=\\\\
=\frac{(x-2)(x+1)}{(x+2)(x-2)}+\frac{x+1}{x+2}=~~~\text{Simplificam prima fractie cu (x - 2).}\\\\
=\frac{x+1}{x+2} + \frac{x+1}{x+2}=\boxed{\frac{2x+2}{x+2}} [/tex]
[tex]\displaystyle\\
E(x)=\frac{2x+2}{x+2}\\\\
\text{Rezolvam ecuatia: }\\
E(x) = 1\\\\
\frac{2x+2}{x+2}=1\\\\
2x+2=x+2\\
2x-x = 2-2\\
\boxed{\bf x = 0}[/tex]
