1÷（5X+4）-1÷（6X-5）=1÷(4X+5)-1÷(5X+4)

1÷（5X+4）-1÷（6X-5）=1÷(4X+5)-1÷(5X+4)
1/(5X+4)-1/(6X-5)=1/(4X+5)-1/(5X+4)
2/(5X+4)=1/(4X+5)+1/(6X-5)
2/(5X+4)=(6X-5+4X+5)/(4X+5)(6X-5)
2/(5X+4)=10X/(4X+5)(6X-5)
10X(5X+4)=2(4X+5)(6X-5)
50X^2+40X=48X^2+20X-50
X^2+10X+25=0
(X+5)^2=0
X=-5 检验 把x=-5代进元方程是它的解
所以元方程的解X=-5

1/(5x+4)-1/(6x-5)=1/(4x+5)-1/(5x+4)
2/(5x+4)=1/(6x-5)+1/(4x+5)
2/(5x+4)=10x/(6x-5)(4x+5)
2(6x-5)(4x+5)=10x(5x+4)
24x^2+10x-25=25x^2+20x
x^2+10x+25=0
(x+5)^2=0
x=-5