Question

thực hiện phép tính:
\(\left(\dfrac{x+y}{x}-\dfrac{2x}{x-y}\right)\dfrac{y-x}{x^2+y^2}\)

Answer 1

\(\left(\dfrac{x+y}{x}-\dfrac{2x}{x-y}\right)\cdot\dfrac{y-x}{x^2+y^2}\)

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

\(=\dfrac{x^2-y^2-2x^2}{x}\cdot\dfrac{-1}{x^2+y^2}\)

\(=\dfrac{-1\left(-x^2-y^2\right)}{x\left(x^2+y^2\right)}=\dfrac{1}{x}\)