Question

Care este rezolvarea exercitiului:E(x)=x²+4x+4 supra x(x+2)/(1+2supra X)

Answer 1

E(x)=$\frac{ x^{2} +4x+4}{ \frac{x(x+2)}{1+ \frac{2}{x} } } = \frac{ (x+2)^{2} }{x(x+2)* \frac{x}{(x+2)} } = \frac{( x+2)^{2} }{ x^{2} }$

Answer 2

E(x) = [x la patrat + 4x + 4 / x(x+2)] / (1+2/x), unde x <> 0 si x + 2 <> 0, deci x <> -2 => (x+2) la patrat / [x(x + 2) inmultit cu (1 + 2/x)] => Se simplifica expresia (x + 2) la patrat de la numarator si expresia (x + 2) de la numitor cu (x + 2). Apoi se aduce la acelasi numitor expresia (1 + 2/x), numitorul comun fiind x. => (x + 2) / [x(x + 2) / x] = (x + 2)x / (x + 2)x = 1.