先化简,再求值【(1/X^2+3X+2)+(1/x^2+5X+6)+1/X^2+7X+12】÷(1/X^2+9X+20)
来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/07/05 12:44:59
先化简,再求值【(1/X^2+3X+2)+(1/x^2+5X+6)+1/X^2+7X+12】÷(1/X^2+9X+20)其中x=根号2
原式={1/((X+1)(X+2))+1/((X+2)(X+3))+1/((X+3)(X+4))}/{1/((X+4)(X+5))}
={1/(X+1)-1/(X+2)+1/(X+2)-1/(X+3)+1/(X+3)-1/(X+4)}/{1/((X+4)(X+5))}
={1/(X+1)-1/(X+4)}/{1/((X+4)(X+5))}
=3/((X+1)(X+4))/{1/((X+4)(X+5))}
=3(X+5)/(X+1)
=3(5+根号2)/(1+根号2)
=(12根号2)-9
={1/(X+1)-1/(X+2)+1/(X+2)-1/(X+3)+1/(X+3)-1/(X+4)}/{1/((X+4)(X+5))}
={1/(X+1)-1/(X+4)}/{1/((X+4)(X+5))}
=3/((X+1)(X+4))/{1/((X+4)(X+5))}
=3(X+5)/(X+1)
=3(5+根号2)/(1+根号2)
=(12根号2)-9
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