Question

Se consideră expresia E(x)=(2x-8/x2-8x+15 - 1/x-3):1/x^2-25 unde x este nr real ... x diferit de -5,,,x diferit de 3,,,, x diferit de 5 Aratati ca E(x)=x+5

Answer 1

$E x_ = ( \frac{2x-8}{x^{2}-8x+15} - \frac{1}{x-3}) : \frac{1}{x^{2} -25} \\ = (\frac{2x-8}{(x-3)(x-5)} - \frac{1}{x-3}) * (x+5)(x-5) \\ = ( \frac{2x-8}{(x-3)(x-5)} - \frac{x+5}{(x-3)(x-5)} ) * (x+5)(x-5)\\ = \frac{2x-8-x+5}{(x-3)(x-5)} *(x+5) (x-5) \\ = \frac{x-3}{(x-3)(x-5)} * (x+5) (x-5) \\ = x+5$