Question

1/(x-y)+1/(x+y)+2x/(x^2+y^2)+4x^3/(x^4+y^4)

化简

Answer 1

原式=2x/(x^2-y^2)+2x/(x^2+y^2)+4x^3/(x^4+y^4)
=4x^3/(x^4-y^4)+4x^3/(x^4+y^4)
=8x^7/(x^8-y^8)

Answer 2

=(x+y)/(x²-y²)+(x-y)/(x²-y²)+2x/(x²+y²)+4x³/(x⁴+y⁴)
=2x/(x²-y²)+2x/(x²+y²)+4x³/(x⁴+y⁴)
=2x(x²+y²)/(x⁴-y⁴)+2x(x²-y²)/(x⁴-y⁴)+4x³/(x⁴+y⁴)
=4x³/(x⁴-y⁴)+4x³/(x⁴+y⁴)
=4x³(x⁴+y⁴)/(x^8-y^8)+4x³(x⁴+y⁴)/(x^8-y^8)
=8x^7/(x^8-y^8)

Answer 3

原式=(x+y+x-y)/(x+y)(x-y)+2x/(x^2+y^2)+4x^3/(x^4+y^4)
=2x/(x^2-y^2)+2x/(x^2+y^2)+4x^3/(x^4+y^4)
=2x(x^2+y^2+x^2-y^2)/(x^2-y^2)(x^2+y^2)+4x^3/(x^4+y^4)
=4x^3/(x^4-y^4)+4x^3/(x^4+y^4)
=4x^3(x^4+y^4+x^4-y^4)/(x^4-y^4)(x^4+y^4)
=8x^7/(x^8-y^8)