原式=1/2( 1/x-1/(x＋2)+1/(x+2)-1/(x+4)+……+1/(x+8)-1/(x+10)）=5/24
所以就有1/x-1/(x+10)=5/12，整理的24=x^2+10x，即x^2+10x-24=0
所以(x-2)(x+12)=0，解得x=2 或x=-12
最后检验知两者都是方程的根
1/2( 1/x-1/(x＋2)+1/(x+2)-1/(x+4)+……+1/(x+8)-1/(x+10)）=5/24
1/x-1/(x+10)=5/12
12*（x+10-x)=5x(x+10)
24=x^2+10x
x^2+10x-24=0
(x-2)(x+12)=0
x=2 或x=-12
经验证x=2或x=-12都是方程的解本回答被提问者和网友采纳
解方程:1\/x(x+2)+1\/(x+2)(x+4)+……+1\/(x+8)(x+10)=5\/24
1\/x(x+2)+1\/(x+2)(x+4)+……+1\/(x+8)(x+10)=5\/241\/(2x)-1\/{2(x+2)) + 1\/{2(x+2)}-1\/{2(x+4)} +……+1\/{2(x+8)} - 1\/{2(x+10)} = 5\/241\/(2x)-1\/{2(x+10)} = 5\/241\/x-1\/(x+10) = 5\/1210\/{x(x+10)} = 5\/122\/{x(x+10)} =.....
解方程:1\/x(x+2)+1\/(x+2)(x+4)+……+1\/(x+8)(x+10)=5\/24
1\/x(x+2)+1\/(x+2)(x+4)+……+1\/(x+8)(x+10)=5\/24 1\/(2x)-1\/{2(x+2)) + 1\/{2(x+2)}-1\/{2(x+4)} +……+1\/{2(x+8)} - 1\/{2(x+10)} = 5\/24 1\/(2x)-1\/{2(x+10)} = 5\/24 1\/x-1\/(x+10) = 5\/12 10\/{x(x+10)} = 5\/12 2\/{x(x+...
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。
解方程:1\/X(X+2)+1\/(X+2)(X+4)+...+1\/(x+8)(x+10)=5\/24
1\/2(1\/x-1\/x+2+1\/x+2-1\/x+4+···-1\/x-10)=5\/24 1\/2(1\/x-1\/x-10)=5\/24 整理得：x²-10x-24=0 (x+2)(x-12)=0 x1=-2舍，x2=12
初二方程求解! 1\/x(x+2)+1\/(x+2)(x+4)+…+1\/(x+8)(x+10)=5\/2
，
...x+2) + 1\/(x+2)(x+3)+..+1\/(x+9)(x+10)=1\/x+10 等类似分母递增的多...
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 ...
解分式方程1\/x(x+2)+1\/(x+2)(x+4)+1\/(x+4)(x+6)=3\/2(x+6)
x+4)(x+6)(x+4+x)\/x(x+2)(x+4)=(3x+12-2)\/2(x+4)(x+6)2\/x(x+4)=(3x+10)\/2(x+4)(x+6)2\/x=(3x+10)\/2(x+6)3x²+10x=4x+24 3x²+6x-24=0 x²+2x-8=0 (x+4)(x-2)=0 ∴x=-4 x=2 检验：x=-4是增根 ∴方程的解是x=2 ...
1\/x(x+2)+1\/(x+2)(x+4)+1\/(x+4)(x+6)=3\/2x+12
这应该是一道解方程吧？题目好像有点问题哦 等号右边应该是3\/(2X+12) 不然算不到整数哦
解方程1\/(x+1)(x+2)+1\/(x+2)(x+3)+……+1\/(x+1994)(x+1995)=2x+3987\/...
(x+2)+1\/(x+2)(x+3)+……+1\/(x+1994)(x+1995)=2x+3987\/3x+5985 {1\/(x+1)-1\/(x+2)}+（1\/(x+2)-1\/(x+3)）+……+{1\/(x+1994)-1\/(x+1995)}=2x+3987\/3x+598 1\/(x+1)-1\/(x+1995)=2x+3987\/3x+598 1994\/（x+1)(x+1995)=(6x^2+1794x+3987)\/3x ...
1\/(x+1)(x+2)+1\/(x+2)(x+3)+1\/(x+3)(x+4)
感觉题最后一个符号应该是负号 则 1\\(x+1)-1\\(x+2)-1\\(x+3)-1\\(x+4)前二项通分后得1\\(x+1)(x+2)后二项通争后得1\\(x+3)(x+4)再进行通分后得（4x+10）\\(x+1)(x+2)(x+3)(x+4)
