Question

Помогите пожалуйста срочно докажите тождество​

Answer 1

Объяснение:

3.

$1)\\\frac{x+y}{x-y} -\frac{x-y}{x+y}=\frac{(x+y)^2-(x-y)^2}{(x-y)*(x+y)}=\frac{x^2+2xy+y^2-(x^2-2xy+y^2)}{x^2-y^2}=\\=\frac{x^2+2xy+y^2-x^2+2xy-y^2}{x^2-y^2} =\frac{4xy}{x^2-y^2}.\\ 2)\\ \frac{x+y}{x-y} +\frac{x-y}{x+y}=\frac{(x+y)^2+(x-y)^2}{(x-y)*(x+y)}=\frac{x^2+2xy+y^2+x^2-2xy+y^2}{x^2-y^2}=\frac{2x^2+2y^2}{x^2-y^2}=\frac{2*(x^2+y^2)}{x^2-y^2} .\\3)\\\frac{4xy}{x^2-y^2}:\frac{2*(x^2+y^2)}{x^2-y^2}=\frac{4xy}{x^2-y^2} *\frac{x^2-y^2}{2*(x^2+y^2)}=\frac{2xy}{x^2+y^2} .$

$4)\\\frac{x^2y^2}{(x+y)^2+(x-y)^2} =\frac{x^2y^2}{x^2+2xy+y^2+x^2-2xy+y^2}=\frac{x^2y^2}{2x^2+2y^2} =\frac{x^2y^2}{2*(x^2+y^2)}.\\ 5)\\\frac{2xy}{x^2+y^2}:\frac{x^2y^2}{2*(x^2+y^2)}=\frac{2xy}{x^2+y^2} *\frac{2*(x^2+y^2)}{x^2y^2}=\frac{4}{xy}.$