早教吧作业答案频道 -->数学-->
化简求值：(x^2-16)/(x^2+8x+16)+x/(x-4)+1/(x^2-16),其中x=（根号下2）+1
题目详情
化简求值：(x^2-16)/(x^2+8x+16)+x/(x-4)+1/(x^2-16),其中x=（根号下2）+1
▼优质解答
答案和解析
(x^2-16)/(x^2+8x+16)+x/(x-4)+1/(x^2-16)
=(x+4)(x-4))/(x+4)^2+x/(x-4)+1/[(x+4)(x-4)]
=(x-4))/(x+4)+x/(x-4)+1/[(x+4)(x-4)]
=[(x-4)^2+x(x+4)+1]/[(x+4)(x-4)]
=(2x^2-4x+17)/(x^2-16)
=[2(x-1)^2+15]/(x^2-16)
x=√2+1
x-1=(√2+1)-1=√2
x^2=(√2+1)^2=3+2√2
(x^2-16)/(x^2+8x+16)+x/(x-4)+1/(x^2-16)
=[2(√2)^2+15]/(3+2√2-16)
=19/(2√2-13)
=19*(2√2+13)/[(2√2-13)*(2√2+13)]
=-(38√2+247)/161
=(x+4)(x-4))/(x+4)^2+x/(x-4)+1/[(x+4)(x-4)]
=(x-4))/(x+4)+x/(x-4)+1/[(x+4)(x-4)]
=[(x-4)^2+x(x+4)+1]/[(x+4)(x-4)]
=(2x^2-4x+17)/(x^2-16)
=[2(x-1)^2+15]/(x^2-16)
x=√2+1
x-1=(√2+1)-1=√2
x^2=(√2+1)^2=3+2√2
(x^2-16)/(x^2+8x+16)+x/(x-4)+1/(x^2-16)
=[2(√2)^2+15]/(3+2√2-16)
=19/(2√2-13)
=19*(2√2+13)/[(2√2-13)*(2√2+13)]
=-(38√2+247)/161
看了化简求值：(x^2-16)/(...的网友还看了以下：
当X取何值,下列各式有意义根号x-1根号2-3x根号x方+1个好1除x根号x+根号-x根号2-x除 2020-04-26 …
二次根式较难题目一道已知,y=根号下1-8x+根号下8x+1+1/2,求代数式根号下x/y+y/x 2020-04-27 …
极限和导数问题已知f(x)连续,f(1+x)-3f(1-x)=8x(1+|sinx|),求f '( 2020-05-17 …
初1的数学题有人会么,商分501.x⒉+-8x⒉-1=2x⒊+7x-32.若(x+1)⒉+4｜y- 2020-06-20 …
急,今天八点钟之前就要,六、求下列函数的定义域：（1）f(x)=3/x+1;(2)f(x)=3/x 2020-07-14 …
解方程.有根号的解方程(1)(5x-3)^2-20又1/4=0(2)4(8x-5)^2=169(3 2020-08-02 …
1.若y=根号x-2010+根号2010-x+1/x,则y等于多少2.若y=根号1-x+根号x-1 2020-08-03 …
1.已知二次根式根号2a+3与根号5是同类二次根式,且满足20＜a＜40,则a可能的取值是?2.已知 2020-12-31 …
当×为何值时,下列各式有意义?(1)根号x+1(2)根号-x(3)根号x^2当×为何值时,下列各式有 2020-12-31 …
下列各组不等中,同解的是A、1/x+根号x＜1+根号x和1/x＜1B、1/x+根号x＜1/x+1和根 2021-02-04 …