神马作文网计算:[(x+2)/(x+3) - (x+1)/(x+2) + (x+4)/(x+5) - (x+3)/(x+4) /
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：2024/11/06 21:41:35
计算:[(x+2)/(x+3) - (x+1)/(x+2) + (x+4)/(x+5) - (x+3)/(x+4) / (x^2 + 7x + 13)/(x^2 + 8x + 15)
[(x+2)/(x+3) - (x+1)/(x+2) + (x+4)/(x+5) - (x+3)/(x+4)] / (x^2 + 7x + 13)/(x^2 + 8x + 15)
=[-1/(x+3)+1/(x+2)-1/(x+5)+1/(x+4)] / (x^2 + 7x + 13)/(x^2 + 8x + 15)
=[(1/(x+4)-1/(x+3))+(1/(x+2)-1/(x+5))]/ (x^2 + 7x + 13)/(x^2 + 8x + 15)
=(-1/(x^2+7x+12)+3/(x^2+7x+10))/ (x^2 + 7x + 13)/(x^2 + 8x + 15)
=[(2x^2+14x+26)/(x+2)(x+3)(x+4)(x+5)]/ [(x^2 + 7x + 13)/(x+3)(x+5)]
=2/(x+2)(x+4)
=[-1/(x+3)+1/(x+2)-1/(x+5)+1/(x+4)] / (x^2 + 7x + 13)/(x^2 + 8x + 15)
=[(1/(x+4)-1/(x+3))+(1/(x+2)-1/(x+5))]/ (x^2 + 7x + 13)/(x^2 + 8x + 15)
=(-1/(x^2+7x+12)+3/(x^2+7x+10))/ (x^2 + 7x + 13)/(x^2 + 8x + 15)
=[(2x^2+14x+26)/(x+2)(x+3)(x+4)(x+5)]/ [(x^2 + 7x + 13)/(x+3)(x+5)]
=2/(x+2)(x+4)
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