作业帮1÷[(x+1)(x+2)]+1÷[(x+2)(x+3)]+…+1÷[(x+2005)(x+2006)]=1/(2x+4012)
来源：学生作业帮助网 编辑：作业帮 时间：2024/05/04 14:15:38
![1÷[(x+1)(x+2)]+1÷[(x+2)(x+3)]+…+1÷[(x+2005)(x+2006)]=1/(2x+4012)](/uploads/image/z/7212924-36-4.jpg?t=1%C3%B7%5B%28x%2B1%29%28x%2B2%29%5D%2B1%C3%B7%5B%28x%2B2%29%28x%2B3%29%5D%2B%E2%80%A6%2B1%C3%B7%5B%28x%2B2005%29%28x%2B2006%29%5D%3D1%2F%282x%2B4012%29)
1÷[(x+1)(x+2)]+1÷[(x+2)(x+3)]+…+1÷[(x+2005)(x+2006)]=1/(2x+4012)
1÷[(x+1)(x+2)]+1÷[(x+2)(x+3)]+…+1÷[(x+2005)(x+2006)]=1/(2x+4012)
1÷[(x+1)(x+2)]+1÷[(x+2)(x+3)]+…+1÷[(x+2005)(x+2006)]=1/(2x+4012)
由于1/（x+i）（x+i+1）可以裂开成1/（x+i)-1/（x+i+1)
所以每一项被裂开成两部分 每项的后一部分和下一项的前一部分地抵消 只有第一项的前一部分和最后一项的后一部分没有被抵消
故原式=1/（x+1）-1/（x+2006）
x-1/x÷(x-1/x)
化简(x^2-2x+1)/(x^2+1)÷(x-1)/(x^2+x)-x
[x^2+2x-8/x^3+2x^2+x]÷[(x-2/x)×(x+4/x+1)]化简[x^2+2x-8/x^3+2x^2+x]÷[(x-2/x)×(x+4/x+1)]化简
【{x²-4x+4/x²-4}-x/x+2】÷x-1/x+2
(x+1-1/1-x)÷(x-x²/x-1) (x-4/x-x-6+ x+2/x-3)÷x+1/x-3
x/x^2-2x÷(x^2-4)^-1
(x²-x+1)÷(x²-x-1)=(x²+x)÷(x²+x-2)解方程
x²-1/x²-2x+1÷x+1/x-1 X 1-x/1+x
计算:2x/(x-2)(x+1)÷(1－x/x+1)-x²+2x/x²-4?
(2x-6)/(x^2-9)+(x^2+2x+1)/(x^2+x-6)÷(x+1)/(x-2)
X^2-3X-2=0,求( x - 2x-1/x )÷(x-1)/(x^2-2x)
(x+2/x^2-2x-x-1/x^2-4x+4)÷4-x/x
[（x+2）/(x²+2x)-(x-1)/(x²-4x+4)]÷(x-4)/x
化简(x^2-1)(x+1)/x^2-x÷(1 +x^2+1/2x)
分式化简1-[(x-1)/x]÷{[x/(x+2)] -[1/(x^2+2x)]}
[x-(x+1分之2x)]÷x²-1分之x²-2x+1
*-----------------------------------------------*| 6 4 X | 8 X X | X X 5 || X X X | X X X | X 7 8 || X X X | X X X | X X X ||---------------+---------------+--------------- || X X X | X X X | 5 1 X || X X X | X 6 X | X X X || 8 X X | 3 5 X | 2 X X ||
化简（x^2-4x+4/2x)÷(x^2-2x/x^2)+1