simplify

1. [(x+2)/(x^2-x-6)] - [(x-4)/(x^2-x-12)] + [(x+3)/(x^2+2x-3)]

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

=[1/(x-3)] - [1/(x+3)] + [1/(x-1)]

=[(x+3-x+3)/x^2-9] + [1/(x-1)]

=[6/x^2-9] + [1/(x-1)]

=(x^2+6x-15)/(x^3-x^2-9x+9)

2007-04-06 12:02:21 補充：
2. [1/(w-x)(x-y)] - [2/(x-y)(y-w)] + [3/(w-x)(w-y)] =[1/(w-x)(x-y)] - [2/(x-y)(y-w)] - [3/(w-x)(y-w)] ={[(y-w)-2(w-x)-3(x-y)]/(w-x)(x-y)(y-w)} =(y-w-2w+2x-3x+3y)/(w-x)(x-y)(y-w) =(4y-x-3w)/(w-x)(x-y)(y-w)

2007-04-06 12:08:50 補充：
3. (x-3/x+3) - (2/x-3) + (3/x^2-9) =(x-3)^2/(x^2-9) - 2(x+3)/(x^2-9) + (3/x^2-9) =[(x-3)^2-2(x+3)+3]/(x^2-9)

2007-04-06 12:10:42 補充：
3. (x-3/x+3) - (2/x-3) + (3/x^2-9)=(x-3)^2/(x^2-9) - 2(x+3)/(x^2-9) + (3/x^2-9)=[(x-3)^2-2(x+3)+3]/(x^2-9) =(x^2-8x+6)/(x^2-9)

1.[(x+2)/(x^2-x-6)] - [(x-4)/(x^2-x-12)] + [(x+3)/(x^2+2x-3)]
=(x+2)/ (X-3)(X+2) – (x-4)/ (x-4) (x+3) + (x+3)/(x+3)(x-1)
=1/ (x-3) – 1/ (x+3) + 1/ (x-1)
=(x+3)(x-1) – (x-3)(x-1)+(x+3)(x-3)/(x-1)(x-3)(x+3)
=x^2+2x-3-x^2+4x-3+x^2-9/(x-1)(x-3)(x+3)
=6x-15+x^2/(x-1)(x-3)(x+3)

2. [1/(w-x)(x-y)] - [2/(x-y)(y-w)] + [3/(w-x)(w-y)]
=1/(w-x)(x-y)+2/(x-y)(w-y)+3/(w-x)(w-y)
=(w-y)+2(w-x)+3(x-y)/(w-x)(w-y)
=(w-y)+2(w-x)+3(x-y)/(w-x)(w-y)(x-y)
=w-y+2w-2x+3x-3y/(w-x)(w-y)(x-y)
=3w+x-4y/(w-x)(w-y)(x-y)

3. (x-3/x+3) - (2/x-3) + (3/x^2-9)
=(x-3)/(x+3) – 2/ (x-3) + 3/ (x-3)(x+3)
=(x-3)^2/(x+3)(x-3) – 2(x+3)/(x+3)(x-3) + 3/(x-3)(x+3)
=(x-3)^2 – 2(x+3) + 3/(x-3)(x+3)
= x^2-6x+9-2x-6+3/(x-3)(x+3)
= x^2-8x+6/ /(x-3)(x+3)