﹙2-x﹚/﹙1-x﹚-﹙4-x﹚/﹙6-x﹚=1-﹙x²-4﹚/﹙x²-7x+6﹚解方程.
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﹙2-x﹚/﹙1-x﹚-﹙4-x﹚/﹙6-x﹚=1-﹙x²-4﹚/﹙x²-7x+6﹚解方程.
﹙2-x﹚/﹙1-x﹚-﹙4-x﹚/﹙6-x﹚=1-﹙x²-4﹚/﹙x²-7x+6﹚
解方程.
﹙2-x﹚/﹙1-x﹚-﹙4-x﹚/﹙6-x﹚=1-﹙x²-4﹚/﹙x²-7x+6﹚解方程.
﹙2-x﹚/﹙1-x﹚-﹙4-x﹚/﹙6-x﹚=1-﹙x²-4﹚/﹙x²-7x+6﹚
整理得
﹙x-2﹚/﹙x-1﹚-﹙x-4﹚/﹙x-6﹚=1-﹙x²-4﹚/﹙x-1﹚(x-6)
两边同时乘以﹙x-1﹚(x-6),得
﹙x-2﹚(x-6)-﹙x-4﹚(x-1)=﹙x-1﹚(x-6)-﹙x²-4﹚
x²-8x+12-(x²-5x+4)=(x²-7x+6)-﹙x²-4﹚
整理得
x=1/2
(2 - x)/ (1 - x) - (4 - x)/ (6 - x) = 1 - (x ² - 4)/ (x ² - 7 x + 6)
(x - 2)/ (x - 1) - (x - 4)/ (x - 6) = 1 - (x + 2)(x - 2)/ (x - 6)(x - 1)
两边乘以 (...
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(2 - x)/ (1 - x) - (4 - x)/ (6 - x) = 1 - (x ² - 4)/ (x ² - 7 x + 6)
(x - 2)/ (x - 1) - (x - 4)/ (x - 6) = 1 - (x + 2)(x - 2)/ (x - 6)(x - 1)
两边乘以 (x - 6)(x - 1)得:
(x - 2)(x - 6) - (x - 4)(x - 1)= (x - 6)(x - 1)- (x + 2)(x - 2)
(x ² - 8 x + 12)- (x ² - 5 x + 4) = (x ² - 7 x + 6)-(x ² - 4)
x ² - 8 x + 12 - x ² + 5 x - 4 = x ² - 7 x + 6 - x ² + 4
- 3 x + 8 = - 7 x + 10
4 x = 2
x = 1 / 2
检验:当 x = 1 / 2 时,(x - 6)(x - 1)≠ 0
∴ x = 1 / 2 是原方程的解
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