Question

Помогите решить. Даю 20 баллов

Answer 1

$\Big(x+y-\dfrac{4xy}{x+y}\Big )\Big (y-x+\dfrac{4xy}{y-x}\Big)=\dfrac{(x+y)^2-4xy}{x+y}\cdot \dfrac{(y-x)^2+4xy}{y-x}=\\\\\\=\dfrac{x^2-2xy+y^2}{x+y}\cdot \dfrac{x^2+2xy+y^2}{y-x}=\dfrac{(x-y)^2\cdot (x+y)^2}{(x+y)(y-x)}=\dfrac{(y-x)^2\cdot (x+y)}{y-x}=\\\\\\=(y-x)(y+x)=y^2-x^2$

$\star \qquad \boxed {\; (a-b)^2=(b-a)^2\; }$