计算:8/(4x^2-1)+(2x+3)/(1-2x)=-1 化简:2x/(x^2+2x+1)+1-x/(x+1)-(x^2-x)/(x^2-1)

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计算:8/(4x^2-1)+(2x+3)/(1-2x)=-1 化简:2x/(x^2+2x+1)+1-x/(x+1)-(x^2-x)/(x^2-1)
计算:8/(4x^2-1)+(2x+3)/(1-2x)=-1

化简:2x/(x^2+2x+1)+1-x/(x+1)-(x^2-x)/(x^2-1)

计算:8/(4x^2-1)+(2x+3)/(1-2x)=-1 化简:2x/(x^2+2x+1)+1-x/(x+1)-(x^2-x)/(x^2-1)
8/(4x^2-1)+(2x+3)/(1-2x)=-1
8/(4x^2-1)-(2x+3)/(2x-1)=-1
8/(4x^2-1)-(2x+3)(2x+1)/(2x-1)(2x+1)=-1
[8-(2x+3)(2x+1)]/(4x^2-1)=-1
8-(4x^2+8x+3)=-(4x^2-1)
-8x+5=1
x=1/2
代入检验,x=1/2使得分母1-2x和4x^2-1=0.舍去
所以原方程无解
2x/(x^2+2x+1)+1-x/(x+1)-(x^2-x)/(x^2-1)
=2x/(x+1)^2+1-x/(x+1)-x(x-1)/[(x+1)(x-1)]
=2x/(x+1)^2+1-x/(x+1)-x/(x+1)
=2x/(x+1)^2+[(x+1)-2x]/(x+1)
=2x/(x+1)^2+(1-x)/(x+1)
=2x/(x+1)^2+(1-x)(x+1)/(x+1)^2
=(2x+1-x^2)/(x+1)^2

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