\(A=\left(\frac{x}{y^2-xy}+\frac{y}{x^2-xy}\right):\left(\frac{x^2-y^2}{x^2y+xy^2}\right)\) điều kiện: \(\left\{\begin{matrix}x,y\ne0\\!x!\ne!y!\end{matrix}\right.\)
\(A=\left(\frac{-x}{y\left(x-y\right)}+\frac{y}{x\left(x-y\right)}\right).\left(\frac{xy\left(x+y\right)}{\left(x-y\right)\left(x+y\right)}\right)=\left(\frac{y}{x\left(x-y\right)}-\frac{x}{y\left(x-y\right)}\right).\left(\frac{xy}{x-y}\right)\)
\(A=\left(\frac{y.xy}{x\left(x-y\right)^2}-\frac{x.xy}{y\left(x-y\right)^2}\right)=\left(\frac{y^2-x^2}{\left(x-y\right)^2}\right)=\frac{\left(y-x\right)\left(y+x\right)}{\left(y-x\right)^2}=\frac{y+x}{y-x}\)
\(\left(\frac{x}{y^2-xy}+\frac{y}{x^2-xy}\right):\frac{x^2-y^2}{x^2y+xy^2}\\ < =>\left(\frac{x}{y\left(y-x\right)}+\frac{y}{x\left(x-y\right)}\right):\frac{\left(x-y\right)\left(x+y\right)}{xy\left(x+y\right)}\\ < =>\left(-\frac{x}{y\left(x-y\right)}+\frac{y}{x\left(x-y\right)}\right):\frac{\left(x-y\right)\left(x+y\right)}{xy\left(x+y\right)}\\ < =>\left(-\frac{x^2}{xy\left(x-y\right)}+\frac{y^2}{xy\left(x-y\right)}\right):\frac{\left(x-y\right)\left(x+y\right)}{xy\left(x+y\right)}\\ < =>\frac{y^2-x^2}{xy\left(x-y\right)}:\frac{\left(x-y\right)\left(x+y\right)}{xy\left(x+y\right)}\\ < =>\frac{-\left(x-y\right)\left(y+x\right)}{xy\left(x-y\right)}:\frac{\left(x-y\right)\left(x+y\right)}{xy\left(x+y\right)}\\ < =>\frac{-\left(x-y\right)\left(y+x\right)}{xy\left(x-y\right)}.\frac{xy\left(x+y\right)}{\left(x-y\right)\left(x+y\right)}\\ \)
\(< =>\frac{-x-y}{x-y}\)
