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1/(x+1)-1/x=1/(x-2)-1/(x-3)(x+8)/(x+7)+(x+9)/(x+8)=(x+10)/(x+9)+(x+7)/(x+6)
题目详情
1/(x+1) - 1/x=1/(x-2) - 1/(x-3)
(x+8)/(x+7) + (x+9)/(x+8)=(x+10)/(x+9) + (x+7)/(x+6)
(x+8)/(x+7) + (x+9)/(x+8)=(x+10)/(x+9) + (x+7)/(x+6)
▼优质解答
答案和解析
1.1/(x+1) - 1/x=1/(x-2) - 1/(x-3)
[x-(x+1)]/x(x+1)=[(x-3)-(x-2)]/(x-3)(x-2)
-1/x(x+1)=-1/(x-3)(x-2)
x(x+1)=(x-3)(x-2)
x^+x=x^-5x+6
6x=6
x=1
2.(x+8)/(x+7) + (x+9)/(x+8)=(x+10)/(x+9) + (x+7)/(x+6)
(x+8)/(x+7) - (x+7)/(x+6)=(x+10)/(x+9)-(x+9)/(x+8)
[(x+8)(x+6)-(x+7)(x+7)]/(x+7)(x+6)=[(x+10)(x+8)-(x+9)(x+9)]/(x+9)(x+8)
-1/(x+7)(x+6)=-1/(x+9)(x+8)
(x+7)(x+6)=(x+9)(x+8)
x^-13x+42=x^+17x+72
-30x=30
x=-1
[x-(x+1)]/x(x+1)=[(x-3)-(x-2)]/(x-3)(x-2)
-1/x(x+1)=-1/(x-3)(x-2)
x(x+1)=(x-3)(x-2)
x^+x=x^-5x+6
6x=6
x=1
2.(x+8)/(x+7) + (x+9)/(x+8)=(x+10)/(x+9) + (x+7)/(x+6)
(x+8)/(x+7) - (x+7)/(x+6)=(x+10)/(x+9)-(x+9)/(x+8)
[(x+8)(x+6)-(x+7)(x+7)]/(x+7)(x+6)=[(x+10)(x+8)-(x+9)(x+9)]/(x+9)(x+8)
-1/(x+7)(x+6)=-1/(x+9)(x+8)
(x+7)(x+6)=(x+9)(x+8)
x^-13x+42=x^+17x+72
-30x=30
x=-1
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