Question

Exercitiul 10,va rog.

Answer 1

Răspuns:

C.

$E(x) = \frac{1}{x+2}$

Explicație pas cu pas:

$E(x) = \Big(\frac{1}{x+2} + \frac{x+1}{x^2 - 4} - \frac{1}{x-2}\Big) : \frac{x^2-9}{x^2 + x - 6}\\ \\ E(x) = \frac{1(x-2) + x+1 - 1(x+2)}{(x-2)(x+2)} : \frac{(x+3)(x-3)}{(x+3)(x-2)}\\ \\ E(x) = \frac{x-2+x+1-x-2}{(x-2)(x+2)} : \frac{x-3}{x-2}\\\\E(x) = \frac{x-3}{(x-2)(x+2)} : \frac{x-3}{x-2}\\\\E(x) = \frac{x-3}{(x-2)(x+2)} \cdot \frac{x-2}{x-3}\\\\E(x) = \frac{1}{x+2}$