一道数学题目- -。化简分式。

一个数学分式化简题~

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

3/(2x+6)-1/(6-2x)+3/(9-x^2)
=3/(2x+6)+1/(2x-6)+3/(9-x^2)
=(3*(2x-6)+2x+6)/(4x^2-36)+3/(9-x^2)
=(6x-18+2x+6)/(4x^2-36)+3/(9-x^2)
=(8x-12)/(4x^2-36)+3/(9-x^2)
=4*(2x-3)/(4*(x^2-9))-3/(x^2-9)
=(2x-3)/(x^2-9)-3/(x^2-9)
=(2x-3-3)/(x^2-9)
=(2x-6)/(x^2-9)
=(2*(x-3))/((x+3)*(x-3))
=2/(x+3)

原式=2(x-3)/(x-2)÷{[5-(x+2)(x-2)]/(x-2)}
=2(x-3)/(x-2)÷[-(x²-9)/(x-2)]
=-2(x-3)/(x-2)×(x-2)/(x+3)(x-3)
=-2[(x-3)/(x-3)][(x-2)/(x-2)][1/(x+3)]
=-2/(x+3)

通分：[(b-c)^3+(c-a)^3+(a-b)^3] / [(a-b)(a-c)(b-c)]
分子简化：[3ab^2-3ac^2+3bc^2+3ca^2-3cb^2-3ba^2] / [(a-b)(a-c)(b-c)]
[ 3ab(b-a)+3ac(a-c)+3bc(c-b) ] / [(a-b)(a-c)(b-c)]
重新拆分得到： 3ab/(a-c)(c-b) + 3ac/(a-b)(b-c) + 3bc/(a-b)(c-a)
前两项提取公因式得到：[3a/(c-b)]*[b/(a-c)-c/(a-b)]+3bc/(a-b)(c-a)
化简： [3a/(c-b)]*[(c-b)(c+b-a)/(a-c)(a-b)] + 3bc/(a-b)(c-a)
中夸号里化简后与3bc/(a-b)(c-a)通分化简
最后可得到： (a-b)(3c-3a) / (a-c)(a-b)
= -3
打这个过程好辛苦，望楼主加分啊~~~~~

同分后，分母=（a-b)(b-c)(c-a)
分子=-(b-c)^3-(c-a)^3-(a-b)^3
=3(b^2c-bc^2+ac^2-a^2c+a^2b-ab^2)
=-3（a-b)(b-c)(c-a)
原式=-3