Question

ma ajuta cineva cu E(x)-ul asta?

Answer 1

$E(x)=\frac{x^2+4x+4}{4x^2+12x+9}*\bigg[2-\frac{2}{(x+2)^2}-^{x+2)}\frac{2x}{x+2}\bigg] \\ \\ E(x)=\frac{(x+2)^2}{(2x+3)^2}*\bigg[\frac{2(x+2)^2}{(x+2)^2}-\frac{2}{(x+2)^2}-\frac{2x(x+2)}{(x+2)^2}\bigg] \\ \\ E(x)=\frac{x+2}{2x+3}*\bigg[\frac{2(x+2)^2-2-\big[2x(x+2)\big]}{(x+2)^2}\bigg] \\ \\ E(x)=\frac{x+2}{2x+3}*\bigg(\frac{2(x+2)^2-2-(2x^2+4x)}{(x+2)^2}\bigg) \\ \\ E(x)=\frac{x+2}{2x+3}*\bigg(\frac{2(x+2)^2-2-2x^2-4x}{(x+2)^2}\bigg) \\ \\ E(x)=\frac{1}{2x+3}*\bigg(\frac{2(x^2+4x+4)-2-2x^2-4x}{x+2}\bigg)$
$E(x)=\frac{1}{2x+3}*\bigg(\frac{2x^2+8x+8-2-2x^2-4x}{x+2}\bigg) \\ \\ E(x)=\frac{1}{2x+3}\frac{4x+6}{x+2} \\ \\ E(x)=\frac{1}{2x+3}*\frac{2(2x+3)}{x+2} \\ \\ E(x)=\frac{2x+3}{x+2}$

4x²+12x+9=
(2x)²+2·2x·3+3²=
(2x+3)²=patrat perfect