1/x+5-1/x+6=1/x+7-1/x+8

1/x+5-1/x+6=1/x+7-1/x+8
1/x+5-1/x+6=1/x+7-1/x+8

1/x+5-1/x+6=1/x+7-1/x+8
1/(x + 5) - 1/(x + 6) = 1/(x + 7) - 1/(x + 8)
1/(x + 5) + 1/(x + 8) = 1/(x + 7) + 1/( x + 6)
( x + 8 + x + 5)/(x + 5)(x + 8) = (x + 6 + x + 7)/(x + 6)(x + 7)
( 2x + 13)/( x^2 + 13x + 40) = ( 2x+ 13)/( x^2 + 13x + 42)
(2x + 13)(x^2 + 13x + 42) = (2x + 13)(x^2 + 13x + 40) = 0
( 2x + 13)( x^2 + 13x + 42) - (2x + 13)(x^2 + 13x + 40) = 0
(2x + 13)( x^2 + 13x + 42 - x^2 - 13x - 40) = 0
2(2x + 13) = 0
要使上式成立,必须有：2x + 13 = 0
x = - 13/2