Question

【急】 初一数学 分式加减

[(a-b)/(a+b-(a+b)/(a-b)]/[1-(a^2+b^2)/(a^2-2ab+b^2)]
[x-x/(x+1)]*[(x+1)/(x^+3x+2)]÷[(x^2-2x)/(x^2-4)]
x/(x+1)-(x+3)/(x-1)÷(x^2-2x+1)/(x^2+4x+3)
b^2/(a+b)÷[a/(a-b)-1]÷[a-a^2/(a+b)]
[(3x-3y)/(y^2-x^2)]+[(x^2-2xy+y^2)/(x^2-y^2)}-[(x^2-x-6)/(x+2)]÷(x+y)

Answer 1

[(a-b)/(a+b)-(a+b)/(a-b)]/[1-(a^2+b^2)/(a^2-2ab+b^2)]
=[(a-b)^2/(a^2-b^2)-(a+b)^2/(a^2-b^2)]/[1-(a^2+b^2)/(a-b)^2]
=[(a-b)^2-(a+b)^2]/[(a^2-b^2)]/[1-(a^2+b^2)/(a-b)^2]
=[(a-b+a+b)(a-b-a-b)]/[(a^2-b^2)]/[1-(a^2+b^2)/(a-b)^2]
=[2a*(-2b)]/[(a^2-b^2)]/[1-(a^2+b^2)/(a-b)^2]
=[-4ab]/[(a^2-b^2)]/{[(a+b)^2-(a^2+b^2)]/(a-b)^2}
=[-4ab]/[(a^2-b^2)]/{[(a^2+b^2+2ab-a^2-b^2)]/(a-b)^2}
=[-4ab]/[(a^2-b^2)]/[2ab/(a-b)^2]
=[-4ab]/[(a^2-b^2)]*(a-b)^2/(2ab)
=(-2)/[(a-b)(a+b)]*(a-b)^2
=(-2)/(a+b)*(a-b)
=-2(a-b)/(a+b)
=2(b-a)/(a+b)

[x-x/(x+1)]*[(x+1)/(x^+3x+2)]÷[(x^2-2x)/(x^2-4)]
=[x(x+1)/(x+1)-x/(x+1)]*[(x+1)/(x+2)(x+1)]÷[x(x-2)/(x-2)(x+2)]
=[x(x+1)/(x+1)-x/(x+1)]*[1/(x+2)]÷[x/(x+2)]
=[x(x+1)-x]/[(x+1)]*[1/(x+2)]÷[x/(x+2)]
=[x^2+x-x]/[(x+1)]*[1/(x+2)]÷[x/(x+2)]
=[x^2/(x+1)]*[1/(x+2)]*(x+2)/x
=[x^2/(x+1)]*1/x
=x/(x+1)

[x/(x+1)-(x+3)/(x-1)]÷(x^2-2x+1)/(x^2+4x+3)
=[x(x+3)/(x^2-1)-(x+3)(x+1)/(x^2-1)÷(x-1)^2/[(x+3)(x+1)]
=[x^2+3x-x^2-4x-1]/(x^2-1)÷(x-1)^2/[(x+3)(x+1)]
=(-x-1)/(x^2-1)÷(x-1)^2/[(x+3)(x+1)]
=-(x+1)/(x-1)(x+1)÷(x-1)^2/[(x+3)(x+1)]
=-1/(x-1)÷(x-1)^2/[(x+3)(x+1)]
=-1/(x-1)*(x+3)(x+1)/(x-1)^2
=-(x+3)(x+1)/(x-1)^3

x/(x+1)-(x+3)/(x-1)*(x^2-2x+1)/(x^2+4x+3)
=x/(x+1)-(x+3)/(x-1)*(x-1)^2/[(x+3)(x+1)]
=x/(x+1)-(x+3)*(x-1)/[(x+3)(x+1)]
=x/(x+1)-(x-1)/(x+1)
=[x-(x-1)]/(x+1)
=[x-x+1]/(x+1)
=1/(x+1)

b^2/(a+b)÷[a/(a-b)-1]÷[a-a^2/(a+b)]
=b^2/(a+b)÷[a/(a-b)-(a-b)/(a-b)]÷[a(a+b)/(a+b)-a^2/(a+b)]
=b^2/(a+b)÷[(a-a+b)/(a-b)]÷[(a^2+ab-a^2)/(a+b)]
=b^2/(a+b)÷[b/(a-b)]÷[ab/(a+b)]
=b^2/(a+b)*(a-b)/b÷[ab/(a+b)]
=b(a-b)/(a+b)÷[ab/(a+b)]
=b(a-b)/(a+b)*(a+b)/ab
=b(a-b)/ab
=(a-b)/a

[(3x-3y)/(y^2-x^2)]+[(x^2-2xy+y^2)/(x^2-y^2)}-[(x^2-x-6)/(x+2)]÷(x+y)
=[-3(x-y)/(x^2-y^2)]+[(x-y)^2/(x-y)(x+y)}-[(x-3)(x+2)/(x+2)]÷(x+y)
=[-3(x-y)/(x-y)(x+y)]+[(x-y)/(x+y)}-(x-3)÷(x+y)
=-3/(x+y)+(x-y)/(x+y)-(x-3)/(x+y)
=[-3+(x-y)-(x-3)]/(x+y)
=[-3+x-y-x+3]/(x+y)
=[3-3+x-x-y]/(x+y)
=-y/(x+y)

Answer 2

=2x+by-3x