Question

(x^2-y^2/x^2+y^2)^3÷(x^+2xy+y^2/x^4-y^4)^2

如题，求过程与结果

Answer 1

((x^2+y^2)/(x^2-y^2))^3÷((x^4-y^4)/(x^2+2xy+y^2))^2
=[(x^2-y^2)^3/(x^2+y^2)^3]/[(x^2+2xy+y^2)^2/(x^4-y^4)^2]
=[(x+y)^3*(x-y)^3/(x^2+y^2)^3]/[(x+y)^4/(x^2+y^2)^2*(x^2-y^2)^2]
=[(x+y)^3*(x-y)^3*(x^2+y^2)^2*(x^2-y^2)^2]/[(x^2+y^2)^3*(x+y)^4]
=[(x+y)^3*(x-y)^3*(x^2+y^2)^2*(x+y)^2*(x-y)^2]/[(x^2+y^2)^3*(x+y)^4]
=[(x-y)^5*(x+y)]/(x^2+y^2)