Question

Se considera expresia ( x - 1 -    x²     ) :   x-2  , unde x este numar real , x ≠ - 2 si x ≠ 2. 
                                             x + 2        x+1
Aratati ca E(x) = 1 , pentru orice numar real x , x ≠ -2 si x ≠ 2 

Dati detali daca puteti ... va rog.
                                             

Answer 1

$[tex]( x-1 - \frac{x^2}{x+2} ) : \frac{x-2}{x+2} \ aducem \ la \ acelasi \ numitor \ in \ paranteza \\ \frac{(x-1)(x+2)-x^2}{x+2} : \frac{x-2}{x+2}= \\ \frac{x^2+2x-x-2-x^2}{x+2} * \frac{x+2}{x-2}= \\ \frac{x-2}{x+2} * \frac{x+2}{x-2} =1 \ prin \ simplificare$

Answer 2

Am vazut poza:

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

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

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