[tex]\displaystyle\\
5)~~~E(x)=\left( \frac{x-2}{x^2 -4}\cdot \frac{5x+10}{x-3} +1 \right)\cdot \frac{x-3}{x+2} =\\\\
=\left( \frac{x-2}{(x -2)(x+2)}\cdot \frac{5(x+2)}{x-3} +1 \right)\cdot \frac{x-3}{x+2} =\\
\text{In paranteza se simplifica (x+2) cu (x+2) si (x-2) cu (x-2)}=\\
=\left( \frac{1}{1}\cdot \frac{5}{x-3} +1 \right)\cdot \frac{x-3}{x+2} =\\\\
=\left( \frac{5}{x-3} +1 \right)\cdot \frac{x-3}{x+2} =\\\\
=\left( \frac{ 1\cdot (x-3)+5}{x-3}\right)\cdot \frac{x-3}{x+2} =
[/tex]
[tex]\displaystyle\\
\left( \frac{ x-3+5}{x-3}\right)\cdot \frac{x-3}{x+2} = \frac{ x+2}{x-3}\cdot \frac{x-3}{x+2} = \boxed{\bf 1}\\\\
\text{S-au simplificat (x+2) cu (x+2) si (x-3) cu (x-3).}[/tex]
