1/x-1/(x+1)+1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+...+1/(x+9)-1/(x+10)=5/12
1/x-1/(x+10)=5/12
10/x(x+10)=5/12
所以x²+10x-24=0
(x+12)(x-2)=0
x=-12,x=2
经检验，x=-12和x=2是方程的解
=1/x-1/(x+1)+1/(x+1)-1/(x+2)+...+1/(x+9)-1/(x+10)
=1/x-1/(x+10)
=9/x(x+10)
=5/12
则5x（x+10）=108
所以：5x^2+50x-108=0
解得：
1/x-1/(x+1)+1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+...+1/(x+9)-1/(x+10)=5/12
1/x-1/(x+10)=5/12
(x+10-x)/x(x+10)=5/12
x(x+10)=24
x=2或x=-12
1/x-1/(x+10)=5/12
x+10-x=5/12·x(x-10)
x1=2,x2=-12
解方程:1\/[x(x+1)]+1\/(x+1)(x+2)+1\/(x+2)(x+3)+...+1\/(x+9)(x+10...
1\/[x(x+1)]+1\/(x+1)(x+2)+1\/(x+2)(x+3)+...+1\/(x+9)(x+10)=5\/12 1\/x-1\/(x+1)+1\/(x+1)-1\/(x+2)+...+1\/(x+9)-1\/(x+10)=5\/12;1\/x-1\/(x+10)=5\/12;12(x+10)-12x=5x(x+10);120=5x²+50x;x²+10x-24=0;(x+12)(x-2)=0;...
解方程:1\/x+1\/x(x+1)+1\/(x+1)(x+2)+1\/(x+2)(x+3)+……+1\/(x+9)(x...
1\/x+1\/x-1\/(x+1)+1\/(x+1)-1\/(x+2)+.+1\/(x+9)-1\/(x+10)=0 2\/x-1\/(x+10)=0 2(x+10)-x=0 x=-20
解方程:1\\(x+10)+1\\(x+1)(x+2)+…+1\\(x+9)(x+10)=2\\5.
1\\(x+10)+1\\(x+1)-1\\(x+2)+…+1\\(x+9)-1\\(x+10)=2\\5.即1\\(x+1)=2\/5 即2x+2=5 解得x=3\/2。
解方程:1\\x(x+1)+1\\(x+1)(x+2)+...+1\/(x+8)(x+9)=2x+3\\x(x+9)_百度...
最后一项是(2x+3)\\x(x+9)还是 2x+3\\x(x+9)若是(2x+3)\\x(x+9)解由1\\x(x+1）+1\\(x+1）（x+2)+...+1\/(x+8)(x+9)=2x+3\\x(x+9)得1\/x-1\/(x+1)+1\/(x+1)-1\/(x+2)+...+1\/(x+8)-1\/(x+9)=2x+3\/x(x+9)即1\/x-1\/(x+9)=(2x+3)\/x(x+9)即...
如何简便化简1\/(x+1)(x+2) + 1\/(x+2)(x+3)+..+1\/(x+9)(x+10)=1\/x+...
这一类的都可以将单项写成两项的差的形势，比如1\/n(n+1)=1\/n - 1\/(n+1)所以题目中的这个式子的左边就等于1\/(x+1) - 1\/(x+2) + 1\/(x+2) - 1\/(x+3) + ... +1\/(x+9) -1\/(x+10)=1\/(x+1) - 1\/(x+10)望采纳 ...
解方程1\/x(x+1)+1\/(x+1)(x+2)+...+1\/(x+8)(x+9)=2x+3\/x(x+9)
1\/x（x+1）+1\/（x+1）（x+2）+...+1\/(x+8)(x+9)=(1\/x - 1\/x+1) + (1\/x+1 - 1\/x+2) + ... + (1\/x+8 - 1\/x+9)=1\/x - 1\/x+9 =9\/x(x+9) = 2x+3\/x(x+9)所以9 = 2x+3 x=3
解方程1\/x(x+1)+1\/(x+1)(x+2)+...+1\/(x+8)(x+9)=2x+3\/x(x+9)?
1\/x（x+1）+1\/（x+1）（x+2）+...+1\/(x+8)(x+9)=(1\/x - 1\/x+1) + (1\/x+1 - 1\/x+2) + ...+ (1\/x+8 - 1\/x+9)=1\/x - 1\/x+9 =9\/x(x+9)= 2x+3\/x(x+9)所以9 = 2x+3 ,2,
解方程:1\/(x+1)(x+2)+1\/(x+3)(x+4)+……+1\/(x+2010)(x+2011)=(2x+401...
∴1\/（x+1)(x+2)+1\/(x+3)(x+4)+……+1\/(x+2010)(x+2011)=1\/（x+1)-1\/(x+2)+1\/(x+3)-1\/(x+4)+...+1\/(x+2010)-1\/(x+2011)=1\/(x+1)-1\/(x+2011)=(2x+4019)\/(3x+6033)∴1\/(x+1)=(2x+4019)\/(3x+6033)+3\/(3x+6033)∴1\/(x+1)=2x+4022\/(3x+6...
1\/x(x+1)(x+2)+1\/(x+1)(x+2)(x+3)...+1\/(x+98)(x+99)(x+100)=?_百度...
x+98)(x+99) - 1\/(x+99)(x+100)]} =(1\/2){1\/x(x+1) - 1\/(x+99)(x+100)} =[(x+99)(x+100) - x(x+1)]\/2x(x+1)(x+99)(x+100)=[198x+9900]\/2x(x+1)(x+99)(x+100)=[99x+4950]\/x(x+1)(x+99)(x+100)=99(x+50)\/x(x+1)(x+99)(x+100)...
解方程:1\/x(x+2)+1\/(x+2)(x+4)+……+1\/(x+8)(x+10)=5\/24(x+10)
解：原式=1\/2(1\/X-1\/(2+X)+1\/(2+x)-1\/(4+X)...+1\/(8+X)-1\/(10+X))=1\/2(1\/X-1\/(10+X))=5\/X(X+10)=5\/24(X+10)解得X=24 这也是一种解题方法，希望你学会。
