观察:1/2=1/1x2=1/1-1/2,1/6=1/2x3=1/2-1/3,1/12=1/3x4=1/3-1/4,...1.观察规律,用含n(n为正整数)的等式表示出来,并证明2.用1的规律计算:1/(x-2)(x-3) - 2/(x-1)(x-3) + 1/(x-1)(x-2)
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![观察:1/2=1/1x2=1/1-1/2,1/6=1/2x3=1/2-1/3,1/12=1/3x4=1/3-1/4,...1.观察规律,用含n(n为正整数)的等式表示出来,并证明2.用1的规律计算:1/(x-2)(x-3) - 2/(x-1)(x-3) + 1/(x-1)(x-2)](/uploads/image/z/8820523-19-3.jpg?t=%E8%A7%82%E5%AF%9F%EF%BC%9A1%2F2%3D1%2F1x2%3D1%2F1-1%2F2%2C1%2F6%3D1%2F2x3%3D1%2F2-1%2F3%2C1%2F12%3D1%2F3x4%3D1%2F3-1%2F4%2C...1.%E8%A7%82%E5%AF%9F%E8%A7%84%E5%BE%8B%2C%E7%94%A8%E5%90%ABn%EF%BC%88n%E4%B8%BA%E6%AD%A3%E6%95%B4%E6%95%B0%EF%BC%89%E7%9A%84%E7%AD%89%E5%BC%8F%E8%A1%A8%E7%A4%BA%E5%87%BA%E6%9D%A5%2C%E5%B9%B6%E8%AF%81%E6%98%8E2.%E7%94%A81%E7%9A%84%E8%A7%84%E5%BE%8B%E8%AE%A1%E7%AE%97%EF%BC%9A1%2F%28x-2%29%28x-3%29+-+2%2F%28x-1%29%28x-3%29+%2B+1%2F%28x-1%29%28x-2%29)
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观察:1/2=1/1x2=1/1-1/2,1/6=1/2x3=1/2-1/3,1/12=1/3x4=1/3-1/4,...1.观察规律,用含n(n为正整数)的等式表示出来,并证明2.用1的规律计算:1/(x-2)(x-3) - 2/(x-1)(x-3) + 1/(x-1)(x-2)
观察:
1/2=1/1x2=1/1-1/2,
1/6=1/2x3=1/2-1/3,
1/12=1/3x4=1/3-1/4,
...
1.观察规律,用含n(n为正整数)的等式表示出来,并证明
2.用1的规律计算:
1/(x-2)(x-3) - 2/(x-1)(x-3) + 1/(x-1)(x-2)
观察:1/2=1/1x2=1/1-1/2,1/6=1/2x3=1/2-1/3,1/12=1/3x4=1/3-1/4,...1.观察规律,用含n(n为正整数)的等式表示出来,并证明2.用1的规律计算:1/(x-2)(x-3) - 2/(x-1)(x-3) + 1/(x-1)(x-2)
1.1/n(n+1)=1/n-1/(n+1)
等式右边=1/n-1/(n+1)
通分=(n+1-n)/n(n+1)=等式左边
所以成立
2.原式=1/(x-3)-1/(x-2)-1/(x-3)+1/(x-1)+1/(x-2)-1/(x-1)
=0
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解方程(x2+x)(x2+x-2)=-1