Question

Rezolvati expresia aceasta

Answer 1

$\mathrm{E(x) = \dfrac{(x+2)^2-9}{x^2-25}:\dfrac{x-1}{x-5} =} \\ \\ \mathrm{= \dfrac{(x+2)^2-3^2}{x^2-25}:\dfrac{x-1}{x-5} =}\\ \\ \mathrm{=\dfrac{\Big[(x+2)-3\Big]\Big[(x+2)+3\Big]}{x^2-5^2}:\dfrac{x-1}{x-5}} = \\ \\\\ =\mathrm{\dfrac{(x-1)(x+5)}{(x-5)(x+5)}\cdot \dfrac{x-5}{x-1}} = \\ \\ \\\mathrm{= \dfrac{(x-5)(x+5)(x-1)}{(x-5)(x+5)(x-1)}} = \\ \\\\ = 1$