我用除法的形式来写了,不然太麻烦了.
x^n表示x的n次方
（1）
x-1 6 10-x
________ + _______-________
x2+3x+2 2+x-x2 4-x2
=（x-1)/[(x+1)(x+2)]-6/[(x-2)(x+1)]+(x-10)/[(x+2)(x-2)]分母因式分解
=[(x-1)(x-2)-6(x+2)+(x-10)(x+1)]/[（x+1)(x+2)(x-2)] 通分
=(x^2-3x+2-6x-12+x^2-9x-10)/[（x+1)(x+2)(x-2)] 把分子乘出来
=(2x^2-18x-20)/[（x+1)(x+2)(x-2)] 化简
=2(x^2-9x-10)/[（x+1)(x+2)(x-2)]
=2(x-10)(x+1)/[（x+1)(x+2)(x-2)] 分子因式分解
=2(x-10)/[(x+2)(x-2)]
=(2x-20）/(x^2-4)
（2） 1 x2
（x+1- _____ )/(x- ___)
1-x x-1
=(x^2-1+1)/(x^2-x-x^2) 分子分母同乘以（x-1)
=x^2/(-x)
=-x
(3)
x2-4 x+2 x+1
(_______ + ______)/ ______
x2-x-6 x-3 x-3
={[(x+2)(x-2)]/[(x-3)(x+2)]+(x+2)/(x-3)}/[(x+1)/(x-3)]
=[(x-2)/(x-3)+(x+2)/(x-3)]/[(x+1)/(x-3)]
=[(x-2)+(x+2)]/（x+1） 分子分母同乘以（x-3）
=2x/(x+1)
(4)
x y2 x的4次方y x2
___ · ___ - ___________________ / _____
x-y x+y x的4次方-y的4次方 x2+y2
=xy^2/(x^2-y^2)-x^2y/(x^2-y^2) 第二部分：除以一个数化成乘以这个数的倒数
=（xy^2-x^2y)/(x^2-y^2)
=xy(y-x)/[(x+y)(x-y)]
=-xy/(x+y）
