解方程:1\x(x+1)+1\(x+1)(x+2)+.+1/(x+8)(x+9)=2x+3\x(x+9)
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解方程:1\x(x+1)+1\(x+1)(x+2)+.+1/(x+8)(x+9)=2x+3\x(x+9)
解方程:1\x(x+1)+1\(x+1)(x+2)+.+1/(x+8)(x+9)=2x+3\x(x+9)
解方程:1\x(x+1)+1\(x+1)(x+2)+.+1/(x+8)(x+9)=2x+3\x(x+9)
由于【(x+1)-x】/x(x+1) =1/x(x+1)
所以1/x(x+1)=1/x-1/(x+1)
同理可得:1/(x+1)(x+2)=1/(x+1)-1/(x+2)·····
所以原方程可写为:【1/x-1/(x+1)】+【1/(x+1)-1/(x+2)】+····【1/(x+8)-1/(x+9)】=2x+3/x(x+9)
去括号得1/x-1/(x+9)=2x+3/x(x+9)