分式计算：x^2-4/x^2+6x+9÷x+2/x+3 a/(a-2)-4a/a^2-4 1/(x-y)-1/(x+y)

x^2-4/x^2+6x+9÷x+2/x+3
=(x²-4)/(x²+6x+9)÷(x+2)/(x+3)
=(x+2)(x-2)/(x+3)²×(x+3)/(x+2)
=(x-2)/(x+3)
a/(a-2)-4a/a^2-4
=a/(a-2)-4a/(a+2)(a-2)
=a(a+2)/(a+2)(a-2)-4a/(a+2)(a-2)
=(a²+2a-4a)/(a+2)(a-2)
=a(a-2)/(a+2)(a-2)
=a/(a+2)
1/(x-y)-1/(x+y)*x^2-2xy+y^2/(y+1)^2-(y-1)^2
=[1/(x-y)-1/(x+y)]×(x²-2xy+y²)/[(y+1)²-(y-1)²]
=[(x+y)/(x-y)(x+y)-(x-y)/(x+y)(x-y)]×(x-y)²/(y+1+y-1)(y+1-y+1)
=(x+y-x+y)/(x+y)(x-y)×(x-y)²/4y
=2y/(x+y)(x-y)×(x-y)²/4y
=(x-y)/2(x+y)