1 1 1 1

题目

1 1 1 1
① —— + —— = —— + ——
X-2 X-6 X-7 X-1
X-4 X-5 X-7 X-8
② —— - —— = —— - ——
X-5 X-6 X-8 X-9

答案

(1)[1/(x-7)]-[1/(x-6)]=[1/(x-2)]-[1/(x-1)]
两边分别通分[1/(x-7)(x-6)]=[1/(x-2)(x-1)]
(x-7)(x-6)=(x-2)(x-1)
x^2-13x+42=x^2-3x+2
10x=40
x=4,代回检验成立
(2)[1+1/(x-5)]-[1+1/(x-6)]=[1+1/(x-8)]-[1+1/(x-9)]
[1/(x-5)]-[1/(x-6)]=[1/(x-8)]-[1/(x-9)]
解法同上,解得x=7,代回检验成立