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化简:1/xy+1/(x+4)(y+4)+1/(x+8)(y+8)+1/(x+12)(y+12)+.1/(x+4n)(y

来源:学生作业帮 编辑:神马作文网作业帮 分类:数学作业 时间:2024/11/19 12:07:10
化简:1/xy+1/(x+4)(y+4)+1/(x+8)(y+8)+1/(x+12)(y+12)+.1/(x+4n)(y+4n)
y=10 x=4 y=2 x=4 y=8 x=4
化简:1/xy+1/(x+4)(y+4)+1/(x+8)(y+8)+1/(x+12)(y+12)+.1/(x+4n)(y
1/xy=(1/x-1/y)*(1/y-x)
1/(x+4)(y+4)=(1/(x+4)-1/(y+4))*(1/y-x)
提取(1/y-x) 原式=( 1/y-x)*(1/x-1/y+1/(x+4)-1/(y+4).1/(x+4n)-1/(y+4n))
因为x=4,y=8
所以 原式=(1/4)*( 1/4 -1/8+1/8 -1/12.1/(4+4n) -1/(8+4n))
=(1/4)*(1/4-1/(8+4n))
=(n+1)/(32+16n)
对x=4,y=10和y=2,x=4类似套就可以了