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(求解、x+5)/(x-1)-(3x-3)/(x+5)=(8x+28)/(x^2+4x-5)-2
题目详情
(求解、x+5)/(x-1)-(3x-3)/(x+5)=(8x+28)/(x^2+4x-5)-2
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答案和解析
(x+5)/(x-1)-(3x-3)/(x+5)=(8x+28)/(x^2+4x-5)-2
(x+5)/(x-1)-(3x-3)/(x+5)-(8x+28)/(x^2+4x-5)=-2
(x+5)^2/(x-1)(x+5)-3(x-1)^2/(x+5)-(8x+28)/(x+5)(x-1)=-2
[(x+5)^2-3(x-1)^2-(8x+28)]/(x+5)(x-1)=-2
[x^2+10x+25-3x^2+6x-3-8x-28]/(x+5)(x-1)=-2
[x^2-3x^2+10x+6x-8x+25-3-28]/(x+5)(x-1)=-2
(-2x^2+8x-6)/(x+5)(x-1)=-2
-2(x^2-4x+3)/(x+5)(x-1)=-2
(x^2-4x+3)/(x+5)(x-1)=1
x^2-4x+3=x^2+4x-5
4x+4x=3+5
8x=8
x=1
经检验x=1是方程的增根,所以方程无解
(x+5)/(x-1)-(3x-3)/(x+5)-(8x+28)/(x^2+4x-5)=-2
(x+5)^2/(x-1)(x+5)-3(x-1)^2/(x+5)-(8x+28)/(x+5)(x-1)=-2
[(x+5)^2-3(x-1)^2-(8x+28)]/(x+5)(x-1)=-2
[x^2+10x+25-3x^2+6x-3-8x-28]/(x+5)(x-1)=-2
[x^2-3x^2+10x+6x-8x+25-3-28]/(x+5)(x-1)=-2
(-2x^2+8x-6)/(x+5)(x-1)=-2
-2(x^2-4x+3)/(x+5)(x-1)=-2
(x^2-4x+3)/(x+5)(x-1)=1
x^2-4x+3=x^2+4x-5
4x+4x=3+5
8x=8
x=1
经检验x=1是方程的增根,所以方程无解
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