Question

Rút gọn : \(\left(x-\dfrac{4xy}{x+y}+y\right):\left(\dfrac{x}{x+y}-\dfrac{y}{y-x}-\dfrac{2xy}{x^2-y^2}\right)\)

Answer 1

\(\left(x-\dfrac{4xy}{x+y}+y\right):\left(\dfrac{x}{x+y}-\dfrac{y}{y-x}-\dfrac{2xy}{x^2-y^2}\right)\)

\(=\left(\dfrac{x\left(x+y\right)-4xy+y\left(x+y\right)}{x+y}\right):\left(\dfrac{x\left(x-y\right)+y\left(x+y\right)-2xy}{x^2-y^2}\right)\)

\(=\dfrac{\left(x-y\right)^2}{x+y}:\dfrac{\left(x-y\right)^2}{x^2-y^2}=\dfrac{\left(x-y\right)^2}{x+y}.\dfrac{\left(x-y\right)\left(x+y\right)}{\left(x-y\right)^2}=x-y\)