Answer:
Given that: [tex]\frac{x-y}{x+y} - \frac{x+y}{x-y}[/tex]
Take LCM of x+y and x-y is, [tex]x^2-y^2[/tex]
then;
[tex]\frac{(x-y)^2 -(x+y)^2}{x^2-y^2}[/tex]
Using the identities rule:
[tex](a+b)^2 = a^2+2ab+b^2[/tex]
[tex]\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}[/tex]
Combine like terms;
[tex]\frac{-4xy}{x^2-y^2}[/tex]
Therefore, the answer is, [tex]\frac{-4xy}{x^2-y^2}[/tex]
