分式数学问题1.已知x+1/y=z+1/x=1,求y+1/z的值2.解方程:(x-4)/(x-5) - (x-5)/(x
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分式数学问题
1.
已知x+1/y=z+1/x=1,求y+1/z的值
2.
解方程:(x-4)/(x-5) - (x-5)/(x-6) = (x-7)/(x-8) - (x-8)(x-9)
1.
已知x+1/y=z+1/x=1,求y+1/z的值
2.
解方程:(x-4)/(x-5) - (x-5)/(x-6) = (x-7)/(x-8) - (x-8)(x-9)
![分式数学问题1.已知x+1/y=z+1/x=1,求y+1/z的值2.解方程:(x-4)/(x-5) - (x-5)/(x](/uploads/image/z/18501029-53-9.jpg?t=%E5%88%86%E5%BC%8F%E6%95%B0%E5%AD%A6%E9%97%AE%E9%A2%981.%E5%B7%B2%E7%9F%A5x%2B1%2Fy%3Dz%2B1%2Fx%3D1%2C%E6%B1%82y%2B1%2Fz%E7%9A%84%E5%80%BC2.%E8%A7%A3%E6%96%B9%E7%A8%8B%EF%BC%9A%28x-4%29%2F%28x-5%29+-+%28x-5%29%2F%28x)
x + 1/y = 1 则:y = 1/(1-x)
z + 1/x = 1 则:z = 1- 1/x = (x-1)/x ,所以,1/z = x/(x-1) = 1+ 1/(x-1) = 1-1/(1-x)
所以 y + 1/z = 1
(x-4)/(x-5) - (x-5)/(x-6) = (x-7)/(x-8) - (x-8)(x-9)
即:1+1/(x-5) - 1 - 1/(x-6) = 1+1/(x-8) - 1 -1/(x-9)
1/(x-5) - 1/(x-6) = 1/(x-8) -1/(x-9)
-1/[(x-5)(x-6)] = -1/[(x-8)(x-9)]
(x-8)(x-9) = (x-5)(x-6)
x²-17x+72 = x²-11x+30
解得:x = 7
z + 1/x = 1 则:z = 1- 1/x = (x-1)/x ,所以,1/z = x/(x-1) = 1+ 1/(x-1) = 1-1/(1-x)
所以 y + 1/z = 1
(x-4)/(x-5) - (x-5)/(x-6) = (x-7)/(x-8) - (x-8)(x-9)
即:1+1/(x-5) - 1 - 1/(x-6) = 1+1/(x-8) - 1 -1/(x-9)
1/(x-5) - 1/(x-6) = 1/(x-8) -1/(x-9)
-1/[(x-5)(x-6)] = -1/[(x-8)(x-9)]
(x-8)(x-9) = (x-5)(x-6)
x²-17x+72 = x²-11x+30
解得:x = 7
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