帮帮忙做下了： 1.化简（x+y)×x^2/(x^2-y^2)+1/(x-y)-(2x^2y-2xy^2)/(x^2-2xy+y^2)

题目

帮帮忙做下了： 1.化简（x+y)×x^2/(x^2-y^2)+1/(x-y)-(2x^2y-2xy^2)/(x^2-2xy+y^2)
2.(x^2-9)/(x^2+5x+6)-(x^2-x-2)/(x^2-2x)+(x^2+2x+4)(x^3-8)

答案

1.化简（x+y)×x^2/(x^2-y^2)+1/(x-y)-(2x^2y-2xy^2)/(x^2-2xy+y^2)
=x^2(x+y)/(x+y)(x-y)+1/(x-y)-2xy(x-y)/(x-y)^2
=x^2/(x-y)+1/(x-y)-2xy/(x-y)
=(x^2-2xy+1)/(x-y)
2.(x^2-9)/(x^2+5x+6)-(x^2-x-2)/(x^2-2x)+(x^2+2x+4)(x^3-8)
=(x+3)(x-3)/(x+3)(x+2)-(x-2)(x+1)/x(x-2)+(x^2+2x+4)/(x-2)(x^2+2x+4)
=(x-3)/(x+2)-(x+1)/x+1/(x+2)
=(x-2)/(x+2)-(x+1)/x
=(x^2-2x-x^2-3x-2)/x(x+2)
=(-5x-2)/x(x+2)
=-(5x+2)/x(x+2)