解方程：7/（x^2)-4/(x-x^2)=(8-x^2）/（x^2-1）+1
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7/x^2 - 4/(x-x^2) = (8-x^2)/(x^2-1) + 1
7/x^2 + 4/(x^2-x) = (8-x^2)/(x^2-1) + 1
7/x^2 + 4/{x(x-1)} = (8-x^2)/{(x+1)(x-1)} + 1
两边同乘以x^2(x+1)(x-1)：
7(x+1)(x-1) + 4x(x+1) = (8-x^2)x^2 + x^2(x+1)(x-1)
7x^2 - 7 + 4x^2 + 4x = 8x^2 - x^4 + x^4 - x^2
4x^2 + 4x - 7 = 0
4(x+1/2)^2 = 7+1
(x+1/2)^2 = 2
x = -1/2 ±√2
7/x^2 + 4/(x^2-x) = (8-x^2)/(x^2-1) + 1
7/x^2 + 4/{x(x-1)} = (8-x^2)/{(x+1)(x-1)} + 1
两边同乘以x^2(x+1)(x-1)：
7(x+1)(x-1) + 4x(x+1) = (8-x^2)x^2 + x^2(x+1)(x-1)
7x^2 - 7 + 4x^2 + 4x = 8x^2 - x^4 + x^4 - x^2
4x^2 + 4x - 7 = 0
4(x+1/2)^2 = 7+1
(x+1/2)^2 = 2
x = -1/2 ±√2
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