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)

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)
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)

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)
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