ĐKXĐ: x2-y2\(\ne\)0 4xy\(\ne\)0
\(\Leftrightarrow\)\(\left(x-y\right)\left(x+y\right)\ne0\) <=>x\(\ne\)0 và y \(\ne\)0
\(\Leftrightarrow x\ne y\) và \(x\ne-y\)
Đặt P= \(\left(\frac{1}{x^2+2xy+y^2}-\frac{1}{x^2-y^2}\right):\frac{4xy}{y^2-x^2}\)
<=>\(\left(\frac{1}{\left(x+y\right)^2}-\frac{1}{\left(x+y\right)\left(x-y\right)}\right).\frac{y^2-x^2}{4xy}\)
<=>\(\left(\frac{x-y}{\left(x+y\right)^2\left(x-y\right)}-\frac{x+y}{\left(x+y\right)^2\left(x-y\right)}\right).\frac{-\left(x^2-y^2\right)}{4xy}\)
<=>\(\frac{x-y-x-y}{\left(x+y\right)^2\left(x-y\right)}.\frac{-\left(x-y\right)\left(x+y\right)}{4xy}=\frac{-2y}{\left(x+y\right)^2\left(x-y\right)}.\frac{-\left(x-y\right)\left(x+y\right)}{4xy}\)
<=>\(\frac{1}{2x\left(x+y\right)}=\frac{1}{2x^2+2xy}\)
