Question

Se considera expresia E(x) = ( 3/x-2 - 2/x+2 - 10/x²-4) : x/x²-3x+2

Answer 1

[tex]E(x)=(\frac{3}{x-2}-\frac{2}{x+2}-\frac{10}{x^2-4}):\frac{x}{x^2-3x+2}\\ \text{Descompunem fiecare numitor in parte:}\\ x^2-4=(x-2)(x+2)\\ x^2-3x+2=x^2-2x-x+2=x(x-2)-(x-2)=(x-2)(x-1)\\ \text{Revenind:}\\ E(x)=(\frac{3}{x-2}-\frac{2}{x+2}-\frac{10}{(x-2)(x+2)})\cdot \frac{(x-2)(x-1)}{x}\\ E(x)=\frac{3(x+2)-2(x-2)-10}{(x-2)(x+2)}\cdot \frac{(x-2)(x-1)}{x}\\ E(x)=\frac{3x+6-2x+4-10}{x+2}\cdot \frac{x-1}{x}\\ E(x)=\frac{\not{x}}{x+2}\cdot \frac{x-1}{\not{x}}\\ [/tex]
${\boxed{\bold{E(x)=\frac{x-1}{x+2},\forall x\in \mathbb{R}-\{0,\pm 2,1\}}}$