The solution of equation (1 / X-2) + (1 / X-5) = (1 / x-3) + (1 / x-4) is x = 7 / 2. The solution of equation (1 / X-7) - (1 / X-5) = (1 / X-6) - (1 / x-4) is x = 11 / 2 (1) The solution of equation (1 / x-a) - (1 / X-B) = (1 / x-C) - (1 / X-D) (a, B, C, d represent different numbers, and a + D = B + C) (2) Using your conjecture, find the solution of (x-1) / (X-2) - (x-3) / (x-4) = (X-2) / (x-3) - (x-4) (X-5)~

The solution of equation (1 / X-2) + (1 / X-5) = (1 / x-3) + (1 / x-4) is x = 7 / 2. The solution of equation (1 / X-7) - (1 / X-5) = (1 / X-6) - (1 / x-4) is x = 11 / 2 (1) The solution of equation (1 / x-a) - (1 / X-B) = (1 / x-C) - (1 / X-D) (a, B, C, d represent different numbers, and a + D = B + C) (2) Using your conjecture, find the solution of (x-1) / (X-2) - (x-3) / (x-4) = (X-2) / (x-3) - (x-4) (X-5)~

(1) X = (a + D) / 2 in the first equation, the sum of the constant terms in the denominators on both sides of the equation is 7, the value of X is 7 / 2, and (1 / x-a) - (1 / X-B) = (1 / x-C) - (1 / X-D) can be transformed into: (1 / x-a) + (1 / X-D) = (1 / x-C) + (1 / X-B), where a + D = B + C, so x = (a + D) / 2 (2) x = 7 / 2 (x-1) / (X-2) - (x-3) / (x -

The solution of equation (x-1 / X-2) - (x-3 / x-4) = (X-2 / x-3) - (x-4 / X-5) is x = 7 / 2, and the solution of equation (1 / X-7) - (1 / X-5) = (1 / X-6) - (1 / x-4) is x = 11 / 2
Solving the equation (1 / X-7) + (1 / x-1) = (1 / X-6) + (1 / X-2)
And (1 / x + a) - (1 / x + b) = (1 / x + C) - (1 / x + D) (a, B, C, d represent different numbers, and a + D = B + C)

(1/x-7)+(1/x-1)=(1/x-6)+(1/x-2)
1/(X-7)-1/(X-6)=1/(X-2)-1/(X-1)
(X-6-X+7)/[(X-7)(X-6)]=(X-1-X+2)/[(X-1)(X-2)]
X-3x + 2 = x-13x + 42
10X=40
X=4
(1/x+a)-(1/x+b)=(1/x+c)-(1/x+d)
(X+B-X-A)/[(X+A)(X+B)]=(X+D-X-C)/[(X+C)(X+D)]
B-A=D-C
X-square + (a + b) x + AB = x-square + (c + D) x + CD
X=(CD-AB)/(A+B-C-D)

The solution of equation (1 / X-2) + (1 / X-5) = (1 / x-3) + (1 / x-4) is x = 7 / 2. The solution of equation (1 / X-7) - (1 / X-5) = (1 / X-6) - (1 / x-4) is x = 11 / 2
Suppose (1) the solution of equation (1 / X-7) + (1 / x-1) = (1 / X-6) + (1 / X-2). (2) the solution of equation (1 / x-a) - (1 / X-B) = (1 / x-C) - (1 / X-D) (a, B, C, d represent different numbers, and a + D = B + C)

By analogy
（1/x-2）+(1/x-5)=(1/x-3)+(1/x-4) x=7/2.【2+5=3+4=7】
(1/x-7)-(1/x-5) = (1/x-6)-(1/x-4) x=11/2.【7+4=5+6=11】
And so on:
The solution of equation (1 / X-7) + (1 / x-1) = (1 / X-6) + (1 / X-2). X = 8 / 2 = 4 [7 + 1 = 6 + 2 = 8]
Solution x = (a + D) / 2 = (B + C) / 2 of equation (1 / x-a) - (1 / X-B) = (1 / x-C) - (1 / X-D) [a + D = B + C]