Question

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)

Answer 1

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)

Answer 2

（x+y)×x^2/(x^2-y^2)+1/(x-y)-(2x^2y-2xy^2)/(x^2-2xy+y^2)

= （x+y)x^2/(x-y)(x+y) + 1/(x-y) - 2xy(x-y)/(x-y)(x-y)

= x^2/(x-y) + 1/(x-y) - 2xy/(x-y)

=(x^2+1-2xy)/(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+1)(x-2)/x(x-2) + (x^2+2x+4)/(x-2)(x^2+2x+4)
=(x-3)/(x+2) - (x+1)/x + 1/(x-2)
=1/x(x+2)(x-2) * (x(x-2)(x-3)-(x+1)(x-2)(x+2)+x(x+2))
=1/x(x+2)(x-2) * ( x^3-5x^2+6x- (x^3-4x+x^2-4 )+(x^2+2x ) )
=1/x(x+2)(x-2) *( -5x^2+12x - 4 )
=-1/x(x+2)(x-2) *(5x-2)(x-2)
= - (5x-2)/x(x+2)
=(2-5x) / (x(x+2))

Answer 3

化简
1.（x+y)×x^2/(x^2-y^2)+1/(x-y)-(2x^2y-2xy^2)/(x^2-2xy+y^2)
=x^2/(x-y)+1/(x-y)-2xy/(x-y)
=(x-1)^2/(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+2)-(x+1)/x+1/(x-2)
=[x(x-3)(x-2)-(x+1)(x^2-4)+x(x+2)]/[x(x^2-4)]
=[x^3-5x^2+6x-x^3-x^2+4x+4+x^2+2x]/[x(x^2-4)]
=[-5x^2+12x+4]/[x(x^2-4)] .

Answer 4

(1)原式=[(x+y)x²]/[(x+y)(x-y)]+1/(x-y)-2xy(x-y)/(x-y)²
=x²/(x-y)+1/(x-y)-2xy/(x-y)
=(x²+1-2xy)/(x-y)
(2)原式=[(x+3)(x-3)]/[(x+2)(x+3)]-[(x-2)(x+1)]/[x(x-2)]+(x²+2x+4)/[(x-2)(x²+2x+4)]
=(x-3)/(x+2)-(x+1)/x+1/(x-2)
=[x(X-2)(x-3)-(X+1)(X+2)(X-2)+X(X+2)]/[x(x+2)(x-2)]
=(-5X²+12x-4)/[x(x+2)(x-2)]
=-(5x-2)(x-2)/[x(x+2)(x-2)]
=(2-5x) / [x(x+2)]

Answer 5

1.（x+y)×x^2/(x^2-y^2)+1/(x-y)-(2x^2y-2xy^2)/(x^2-2xy+y^2)
=(x+y)×x^2/(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+1-2xy)/(x-y)
=(x-y)^2/(x-y)
=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+2)(x+3)-(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)