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分式加减计算题X+2 X^2-2X+1 2X-6---X-------- - ---- X-1 X^2-X-6 X^2-9X^2-1 1----- + X(1+ - )X-1 X 其中X=(根号2) - 1

分类: 作业答案 • 2021-12-19 15:55:03
问题描述：

分式加减计算题
X+2 X^2-2X+1 2X-6
---X-------- - ----
X-1 X^2-X-6 X^2-9
X^2-1 1
----- + X(1+ - )
X-1 X 其中X=(根号2) - 1

答

看不懂耶

答

[(x+2)/(x-1)]*[(x^2-2x+1)/(x^2-x-6)]-(2x-6)/(x^2-9)
=[(x+2)/(x-1)]*[(x-1)^2/(x-3)(x+2)]-2(x-3)/(x+3)(x-3)
=(x+2)(x-1)^2/[(x-1)(x-3)(x+2)]-2/(x+3)
=(x-1)/(x-3)-2/(x+3)
=[(x-1)(x+3)-2(x-3)]/(x+3)(x-3)
=(x^2+2x-3-2x+6)/(x+3)(x-3)
=(x^2+3)/(x+3)(x-3)
(x^2-1)/(x-1)+x(1+1/x)
=(x+1)(x-1)/(x-1)+x+1
=x+1+x+1
=2x+2
=2根号2-2+2
=2根号2

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