Упростите выражения (4xy)/(y^(2)-x^(2) : (1)/(y^(2)-x^(2) + (1)/x^(2)+2xy-y^(2

Question

Упростите выражения (4xy)/(y^(2)-x^(2) : (1)/(y^(2)-x^(2) + (1)/x^(2)+2xy-y^(2

Answer 1

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

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

=4xy/(y^2-x^2) : ((y-x+y+x)/((y+x)^2*(y-x))=

=4xy/(y^2-x^2) :(2y/((y+x)^2*(y-x))=

=(4xy*(y+x)^2*(y-x))/(2y*(y^2-x^2))=

=2x*(y+x)^2*(y-x))/((y-x)(y+x))=

2x(y+x)