Question

Fie expresia E(X) = $\frac{ x^{2} -x-2}{ x^{2} -4}$ + $\frac{x+1}{x+2}$. Determinați valorile reale ale lui x, pentru care E(X) = 1.

Answer 1

$\frac{ x^{2} -2x+x-2}{(x-2)(x+2)} + \frac{x+1}{x+2} =1$
$\frac{x(x-2)+(x-2)}{(x-2)(x+2)} + \frac{x+1}{x+2} =1$
$\frac{(x-2)(x+1)}{(x-2)(x+2)} + \frac{x+1}{x+2} =1$
$\frac{x+1}{x+2}+ \frac{x+1}{x+2} =1$
2x+2=x+2
x=0