(16x-13)/(4x-3)+(40x-43)/(8x-9)=(32x-30)/(8x-7)+(20x-24)/(4x-5)....
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(16x-13)/(4x-3)+(40x-43)/(8x-9)=(32x-30)/(8x-7)+(20x-24)/(4x-5)....
(16x-13)/(4x-3)+(40x-43)/(8x-9)=(32x-30)/(8x-7)+(20x-24)/(4x-5)
....
(16x-13)/(4x-3)+(40x-43)/(8x-9)=(32x-30)/(8x-7)+(20x-24)/(4x-5)....
(16x-13)/(4x-3)+(40x-43)/(8x-9)=(32x-30)/(8x-7)+(20x-24)/(4x-5)
4-1/(4x-3)+5+2/(8x-9)=4-2/(8x-7)+5+1/(4x-5)
2/(8x-9)+2/(8x-7)=1/(4x-3)+1/(4x-5)
2(8x-9+8x-7)/[(8x-9)(8x-7)]=(4x-3+4x-5)/[(4x-3)(4x-5)]
2(16x-16)/[(8x-9)(8x-7)]=(8x-8)/[(4x-3)(4x-5)]
其中x=1时等式恒成立
若x≠1时可化为
4(4x-3)(4x-5)=(8x-9)(8x-7)
64x²-128x+60=64x²-128x+63
等式不成立
所以方程的解为x=1
(4(4x-3)-1)/4x-3 + (5(8x-9)+2)/(8x-9) =(4(8x-7)-2)/(8x-7) +(5(4x-5)+1)/(4x-5)
整理得
2/(8x-9) - 1/4x-3 = 1/(4x-5) - 1/(8x-7)
两边分别通分得
1/(4x-5)(8x-7) = 1/(8x-9)(4x-3)
化简
(4x-5)(8x-7) = (8x-9)(4x-3)
化简
x=1