x+2/x+1-x+3/x+2-x+4/x+3+x+5/x+4

来源:学生作业帮助网 编辑:作业帮 时间:2024/03/28 20:55:51
x+2/x+1-x+3/x+2-x+4/x+3+x+5/x+4

x+2/x+1-x+3/x+2-x+4/x+3+x+5/x+4
x+2/x+1-x+3/x+2-x+4/x+3+x+5/x+4

x+2/x+1-x+3/x+2-x+4/x+3+x+5/x+4

(x+2)/(x+1)-(x+3)/(x+2)-(x+4)/(x+3)+(x+5)/(x+4)
=1+1/(x+1)-1-1/(x+2)-1-1/(x+3)+1+1/(x+4)
=1/(x+1)-1/(x+2)-1/(x+3)+1/(x+4)
=[(x+2)-(x+1)]/[(x+1)(x+2)]-[(x+4)-(x+3)]/[(x+3)(x+4)]
=1/[(x+1)(x+2)]-1/[(x+3)(x+4)]
=[(x+3)(x+4)-(x+1)(x+2)]/[(x+1)(x+2)(x+3)(x+4)]
=(4x+10)/[(x+1(x+2)(x+3)(x+4)]

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