Question

E(x)=
$(x - 2 - \frac{ {x}^{2} - 4}{x + 3} ) \div \frac{x - 2}{x + 3}$
Aduceti expresia la forma ei cea mai simpla​

Answer 1

 

$\displaystyle\bf\\E(x)=\left(x - 2 - \frac{ {x}^{2} - 4}{x + 3}\right) : \frac{x - 2}{x + 3}\\\\\\E(x)=\left(\frac{x - 2}{1} - \frac{ {x}^{2} - 4}{x + 3}\right) : \frac{x - 2}{x + 3}\\\\\\E(x)=\left(\frac{x - 2}{1} - \frac{ {x}^{2} - 4}{x + 3}\right) : \frac{x - 2}{x + 3}\\\\\\E(x)=\left(\frac{(x - 2)(x + 3)}{x + 3} - \frac{ {x}^{2} - 4}{x + 3}\right) : \frac{x - 2}{x + 3}\\\\\\E(x)=\left(\frac{x^2+x-6}{x + 3} - \frac{ {x}^{2} - 4}{x + 3}\right) : \frac{x - 2}{x + 3}$

.

$\displaystyle\bf\\E(x)=\frac{x^2+x-6-x^2+4}{x + 3} : \frac{x - 2}{x + 3}\\\\\\E(x)=\frac{x-6+4}{x + 3} : \frac{x - 2}{x + 3}\\\\\\E(x)=\frac{x-2}{x + 3} : \frac{x - 2}{x + 3}\\\\\\E(x)=\frac{x-2}{x + 3} \cdot \frac{x +3}{x - 2}\\\\\\E(x)=\frac{(x-2)(x +3)}{(x + 3)(x - 2)}\\\\Se~fac~simplificari.\\\\\boxed{\bf E(x)=1}$