Tìm giá trị phân thức A = 3x-2y/ 3x+2y

* Hướng dẫn giải

$2\mathrm{y}<3\mathrm{x}<0\Rightarrow 2\mathrm{y}-3\mathrm{x}>0\Rightarrow \left\{\begin{array}{l}3\mathrm{x}-2\mathrm{y}<0\\ 3\mathrm{x}+2\mathrm{y}<0\end{array}\right.\Rightarrow \mathrm{A}>0$

$\begin{array}{l}\mathrm{A}=\frac{3\mathrm{x}-2\mathrm{y}}{3\mathrm{x}+2\mathrm{y}}\Rightarrow {\mathrm{A}}^2=\frac{{\left(3\mathrm{x}-2\mathrm{y}\right)}^2}{{\left(3\mathrm{x}+2\mathrm{y}\right)}^2}=\frac{9{\mathrm{x}}^2+4{\mathrm{y}}^2-12\mathrm{xy}}{9{\mathrm{x}}^2+4{\mathrm{y}}^2+12\mathrm{xy}}\\ =\frac{20\mathrm{xy}-12\mathrm{xy}}{20\mathrm{xy}+12\mathrm{xy}}=\frac{8\mathrm{xy}}{32\mathrm{xy}}=\frac{1}{4}\Rightarrow \mathrm{A}=\pm \frac{1}{2}\end{array}$

Mà $\mathrm{A}>0\Rightarrow \mathrm{A}=\frac{1}{2}$