[(x+2)/(x+3)-(x+1)/(x+2)+(x+4)/(x+5)-(x+3)/(x+4)]/[(x的平方+7x+13)/(x的平方+8x+15)]

来源:学生作业帮助网 编辑:作业帮 时间:2022/12/02 18:05:14
[(x+2)/(x+3)-(x+1)/(x+2)+(x+4)/(x+5)-(x+3)/(x+4)]/[(x的平方+7x+13)/(x的平方+8x+15)]

[(x+2)/(x+3)-(x+1)/(x+2)+(x+4)/(x+5)-(x+3)/(x+4)]/[(x的平方+7x+13)/(x的平方+8x+15)]
[(x+2)/(x+3)-(x+1)/(x+2)+(x+4)/(x+5)-(x+3)/(x+4)]/[(x的平方+7x+13)/(x的平方+8x+15)]

[(x+2)/(x+3)-(x+1)/(x+2)+(x+4)/(x+5)-(x+3)/(x+4)]/[(x的平方+7x+13)/(x的平方+8x+15)]
(x+2)/(x+3)-(x+1)/(x+2)+(x+4)/(x+5)-(x+3)/(x+4)
=[1-1/(x+3)]-[1-1/(x+2)]+[1-1/(x+5)]-[1-1/(x+4)]
=1/(x+2)-1/(x+3)+1/(x+4)-1/(x+5)
=(x+3-x-2)/(x+2)(x+3)+(x+5-x-4)/(x+4)(x+5)
=1/(x^2+5x+6)+1/(x^2+9x+20)
=(2x^2+14x+26)/(x+2)(x+3)(x+4)(x+5)
=2(x^2+7x+13)/(x+2)(x+3)(x+4)(x+5)
x^2+8x+15=(x+3)(x+5)
所以原式=[2(x^2+7x+13)/(x+2)(x+3)(x+4)(x+5)]*[(x+3)(x+5)/(x^2+7x+13)]
=2/(x+2)(x+4)
=2/(x^2+6x+8)

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