【急】3道七年级数学题目(特殊分式）

显示全部楼层 · 2009-12-9 21:23:25

①1/1*2+1/2*3+1/3*4+……91/98*99+1/99*1001/1*2+1/2*3+1/3*4+……91/98*99+1/99*100=1-1/2+1/2-1/3+1/3-1/4+....+1/99-1/100=1-1/100=99/100②化简下列算是：1/x+1/x(x+1)+1/(x+1)(x+2)+……+1/(x+2004)(x+2005)1/x+1/x(x+1)+1/(x+1)(x+2)+……+1/(x+2004)(x+2005)=1/x+1/x-1/(x+1)+1/(x+1)-.....+1/(x+2004)-1/(x+2005)=2/x-1/(x+2005)=(x+4010)/x(x+2005)③求下列分式方程1/x(x+2)+1/(x+2)(x+4)-1/2x=11/x(x+2)+1/(x+2)(x+4)-1/2x=11/2x-1/2(x+2)+1/2(x+2)-1/2(x+4)-1/2x=12(x+4)=-1x=-9/2

千问 · 2009-12-9 21:23:25

①1/1*2+1/2*3+1/3*4+……91/98*99+1/99*100=(1-1/2)+(1/2-1/3)+(1/3-1/4)+...+(1/99-1/100)=1-1/100=99/100②1/x+1/x(x+1)+1/(x+1)(x+2)+……+1/(x+2004)(x+2005)=1/x+[1/x-1/(x+1)]+[1/(x+1)-1/(x+2)]+...+[1/(x+2004)-1/(x+2005)]=2/x -1/(x+2005)=(x+4010)/[x(x+2005)]③ 1/x(x+2)+1/(x+2)(x+4)-1/2x=1[1/x-1/(x+2)+1/(x+2)-1/(x+4)]/2-1/2x=11/2x-1/2(x+4)-1/2x=1-1/2(x+4)=12(x+4)=-1x+4=-1/2x=-4-1/2=-9/2

千问 · 2009-12-9 21:23:25

①1/1*2+1/2*3+1/3*4+……91/98*99+1/99*100分析：1/1*2=1-1/2
1/2*3=1/2-1/3
1/3*4=1/3-1/4……
1/98*99=1/98-1/99
1/99*100=1/99-1/100所以原式=1-1/2+1/2-1/3+1/3-1/4……1/99-1/100=1-1/100=99/100②化简下列算是：1/x+1/x(x+1)+1/(x+1)(x+2)+……+1/(x+2004)(x+2005)分析：与上题方式相同，得：1/x+1/x-1/x+2005=2/x-1/x+2005=x-4010/x^2+2005x③求下列分式方程1/x(x+2)+1/(x+2)(x+4)-1/2x=1这题也要用上面方式来转换：解：(1/x-1/x+2)*1/2+(1/x+2-1/x+4)*1/2-1/2x=1
1/2x-1/2x+4+1/2x+4-1/2x+8-1/2x=1 -1/2x+8=12x+8=-12x=-9x=-9/2

千问 · 2009-12-9 21:23:25

①1/1*2+1/2*3+1/3*4+…+1/9*10=解：1/(1*2)=1/1-1/21/(2*3)=1/2-1/31/(3*4)=1/3-1/4::1/(99*100)=1/99-1/100所以原式=(1/1-1/2)+……+（1/99-1/100）=99/100

千问 · 2009-12-9 21:23:25

1.
99/100 2.
2004/x1、原式=（1-1/2）+（1/2-1/3）+（1/3-1/4）+…………+（1/98-1/99）+(1/99-1/100)=1-1/100=99/100