12x-10/(4x-3)-(32x-34/8x-9)=(24x-23/8x-7)+(16x-19/4x-5)
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原方程可化为
3-1/(4x-3)+4+2/(8x-9)=3-2/(8x-7)+4+1/(4x-5)
于是2/(8x-9)-1/(4x-3)=1/(4x-5)-2/(8x-7)
移项得，2/(8x-9) +2/(8x-7)=1/(4x-5)+1/(4x-3)
令4x-4=y，则有2/(2y-1)+2/(2y+1)=1/(y-1)+1/(y+1)
两边通分得，[2(2y+1)+2(2y-1)]/(2y+1)(2y-1)=(y+1+y-1)/(y+1)(y-1)
8y/(2y+1)(2y-1)=2y/(y+1)(y-1)
8y(y+1)(y-1)=2y(2y+1)(2y-1)
8y(y^2-1)=2y(4y^2-1)
8y^3-8y=8y^3-2y
6y=0 y=0 于是4x-4=0 x=1
3-1/(4x-3)+4+2/(8x-9)=3-2/(8x-7)+4+1/(4x-5)
于是2/(8x-9)-1/(4x-3)=1/(4x-5)-2/(8x-7)
移项得，2/(8x-9) +2/(8x-7)=1/(4x-5)+1/(4x-3)
令4x-4=y，则有2/(2y-1)+2/(2y+1)=1/(y-1)+1/(y+1)
两边通分得，[2(2y+1)+2(2y-1)]/(2y+1)(2y-1)=(y+1+y-1)/(y+1)(y-1)
8y/(2y+1)(2y-1)=2y/(y+1)(y-1)
8y(y+1)(y-1)=2y(2y+1)(2y-1)
8y(y^2-1)=2y(4y^2-1)
8y^3-8y=8y^3-2y
6y=0 y=0 于是4x-4=0 x=1
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