Question

Aduceti expresia din imagine la forma cea mai simpla 

Answer 1

$E(x)=( \frac{2x}{x-1}- \frac{x}{x+1})* \frac{x^3+2x^2+x}{x^3+3x^2} \\ E(x)=\frac{2x(x+1)-x(x-1)}{(x-1)(x+1)}*\frac{x(x^2+2x+1)}{x^2(x+3)} \\ E(x)=\frac{2x^2+2x-x^2+x}{(x-1)(x+1)}*\frac{x(x+1)^2}{x^2(x+3)} \\ E(x)=\frac{x^2+3x}{(x-1)}*\frac{(x+1)}{x(x+3)} = \frac{x(x+3)}{(x-1)}*\frac{(x+1)}{x(x+3)} \\ E(x)=\frac{x+1}{x-1}$