A= \(\left[\dfrac{1}{x^2+2xy+y^2}-\dfrac{1}{x^2-y^2}\right]:\dfrac{4xy}{y^2-x^2}\)
\(=\left[\dfrac{1}{\left(x+y\right)^2}+\dfrac{1}{y^2-x^2}\right]:\dfrac{4xy}{y^2-x^2}\)
=\(\left[\dfrac{1}{\left(x+y\right)^2}+\dfrac{1}{\left(y-x\right)\left(y+x\right)}\right]:\dfrac{4xy}{y^2-x^2}\)
=\(\left[\dfrac{y-x}{\left(x+y\right)^2.\left(y-x\right)}+\dfrac{y+x}{\left(x+y\right)^2\left(y-x\right)}\right]:\dfrac{4xy}{y^2-x^2}\)
=\(\left[\dfrac{y-x+y+x}{\left(x+y\right)^2\left(y-x\right)}\right]:\dfrac{4xy}{y^2-x^2}\)
\(=\dfrac{2y}{\left(x+y\right)^2\left(y-x\right)}:\dfrac{4xy}{y^2-x^2}\)
=\(\dfrac{2y.\left(y-x\right)\left(y+x\right)}{\left(x+y\right)^2\left(y-x\right)4xy}\)
=\(\dfrac{1}{\left(x+y\right)2x}\)
=\(\dfrac{1}{2x^2+2xy}\)
