ĐKXĐ: \(x\ne\pm y\)
VT=\(\left(\dfrac{2xy}{x^2-y^2}+\dfrac{x-y}{2x+2y}\right)\cdot\dfrac{2x}{x+y}+\dfrac{y}{y-x}\)
\(=\left(\dfrac{2xy}{\left(x-y\right)\left(x+y\right)}+\dfrac{x-y}{2\left(x+y\right)}\right)\cdot\dfrac{2x}{x+y}-\dfrac{y}{x-y}\)
\(=\dfrac{4xy+\left(x-y\right)^2}{2\left(x-y\right)\left(x+y\right)}\cdot\dfrac{2x}{x+y}-\dfrac{y}{x-y}\)
\(=\dfrac{\left(x+y\right)^2\cdot x}{\left(x-y\right)\cdot\left(x+y\right)^2}-\dfrac{y}{x-y}\)
\(=\dfrac{x}{x-y}-\dfrac{y}{x-y}=\dfrac{x-y}{x-y}=1\)=VP
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