(1)(5-x)/(x-4)+1/(4-x)=1
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(1)(5-x)/(x-4)+1/(4-x)=1
(2)1/(x^3+2x^2+x) + 1/(x^2+2x+1) =5/(2^2+2x)
(3)(1-x)/(1+x+x^2) + 6/(1-x)=7/(1-x)
(4)52/(x-8)=48/x + 4/(x-26)
(2)1/(x^3+2x^2+x) + 1/(x^2+2x+1) =5/(2^2+2x)
(3)(1-x)/(1+x+x^2) + 6/(1-x)=7/(1-x)
(4)52/(x-8)=48/x + 4/(x-26)
解(5-x)/(x-4)+1/(4-x)=1
(5-x)/(x-4)-1/(x-4)=1
(5-x)/(x-4)*(X-4)-1/(x-4)*(X-4)=1
5-x-1=x-4
2x=8
x=4
经检验,x=4,为增根
所以方程无解
(2) 1/x(x+1)^2+1/(x+1)^2=5/2x(x+1)
1/x(x+1)^2*2x(x+1)^2+1/(x+1)^2*2x(x+1)^2=5/2x(x+1)*2x(x+1)^2
2+2x=5(x+1)
2+2x=5x+5
3x=-3
x=-1
经检验x=-1是增根
所以方程无解
(3)
(1-x)^2/(1+x+x^2)=1
x^2+x+1=x^2-2x+1
x+1=-2x+1
x=0
经检验X=0为原方程的根
(4)52/(x-8)=48/x + 4/(x-26)
52/(x-8)*x(x-8)(x-26) =48/x*x(x-8)(x-26) + 4/(x-26)*x(x-8)(x-26)
52x(x-26)=48(x-8)(x-26)+4x(x-8)
13x(x-26)=12(x-8)(x-26)+x(x-8)
13x^2-338x=12(x^2-34x+208)+(x^2-8x)
13x^2-338x=12x^2-408x+2496+x^2-8x
-338x=-408x+2496-8x
408x+8x-338x=2496
78x=2496
x=32
经检验,x=32是原方程的根
(5-x)/(x-4)-1/(x-4)=1
(5-x)/(x-4)*(X-4)-1/(x-4)*(X-4)=1
5-x-1=x-4
2x=8
x=4
经检验,x=4,为增根
所以方程无解
(2) 1/x(x+1)^2+1/(x+1)^2=5/2x(x+1)
1/x(x+1)^2*2x(x+1)^2+1/(x+1)^2*2x(x+1)^2=5/2x(x+1)*2x(x+1)^2
2+2x=5(x+1)
2+2x=5x+5
3x=-3
x=-1
经检验x=-1是增根
所以方程无解
(3)
(1-x)^2/(1+x+x^2)=1
x^2+x+1=x^2-2x+1
x+1=-2x+1
x=0
经检验X=0为原方程的根
(4)52/(x-8)=48/x + 4/(x-26)
52/(x-8)*x(x-8)(x-26) =48/x*x(x-8)(x-26) + 4/(x-26)*x(x-8)(x-26)
52x(x-26)=48(x-8)(x-26)+4x(x-8)
13x(x-26)=12(x-8)(x-26)+x(x-8)
13x^2-338x=12(x^2-34x+208)+(x^2-8x)
13x^2-338x=12x^2-408x+2496+x^2-8x
-338x=-408x+2496-8x
408x+8x-338x=2496
78x=2496
x=32
经检验,x=32是原方程的根
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