Question

4xy дробь y^2-x^2/(1 дробь y^2-x^2+1 дробь x^2+2xy+y^2)

Answer 1

$\frac{4xy}{y^2-x^2}:( \frac{1}{y^2-x^2}+ \frac{1}{x^2+2xy+y^2})= \frac{4xy}{(y-x)(y+x)}:( \frac{1}{(y-x)(y+x)}+ \frac{1}{(y+x)^2})= \\ \\ \frac{4xy}{(y-x)(y+x)}:( \frac{1}{(y-x)(y+x)}+ \frac{1}{(y+x)(y+x)})= \frac{4xy}{(y-x)(y+x)}: \frac{(y+x)+(y-x)}{(y-x)(y+x)(y+x)}= \\ \\ \frac{4xy}{(y-x)(y+x)}* \frac{(y-x)(y+x)(y+x)}{y+x+y-x}= \frac{4xy(y+x)}{y^2}= \frac{4xy+4x^2}{y}$