作业帮莫一笔带过 小弟这道题实在不懂..
来源：学生作业帮助网 编辑：作业帮 时间：2024/05/10 14:33:06
莫一笔带过 小弟这道题实在不懂..
莫一笔带过 小弟这道题实在不懂..
莫一笔带过 小弟这道题实在不懂..
[x－x²/(x＋1)]÷[1＋x²/(1－x²)]
＝[(x(x＋1)－x²)/(x＋1)]÷[(1－x²＋x²)/(1－x²)]
＝[x/(x＋1)]÷[1/(1－x²)]
＝[x/(x＋1)]×(1－x²)
＝[x/(x＋1)]×(1－x)(1＋x)
＝x(1－x)
当x＝1＋√2时,原式＝(1＋√2)×[1－(1＋√2)]＝－√2－2.
x- x^2/(x+1) = (x^2 - x -x^2 )/(x+1) = -x/(x+1)
1+x^2/(1-x^2) = (1-x^2+x^2)/(1-x^2)=1/(1-x^2) = 1/((1-x)(1+x))
于是原式=-x/(x+1) / (1/((1-x)(1+x))) = -x/(x+1) *(1-x)(1+x) = -x * (1-x) = x*(x-1)
全部展开
x- x^2/(x+1) = (x^2 - x -x^2 )/(x+1) = -x/(x+1)
1+x^2/(1-x^2) = (1-x^2+x^2)/(1-x^2)=1/(1-x^2) = 1/((1-x)(1+x))
于是原式=-x/(x+1) / (1/((1-x)(1+x))) = -x/(x+1) *(1-x)(1+x) = -x * (1-x) = x*(x-1)
=(1+sqrt2)(1+sqrt2-1) = (1+sqrt2)*sqrt2=sqrt2+2
sqrt是根号
收起
过程在图上
原式=[x(x+1)/x+1-x^2/x+1]/[1/x^2/1-x^2+x^2/1-x^2]
=x/x+1*(1+x)(1-x)
=x(1-x)
=-√2(1+√2)
=-√2-2
[x－x²/(x＋1)]÷[1＋x²/(1－x²)]
=（x²+x-x²)/(x+1)÷(1-x²+x²)/(1+x)(1-x)
=x/(x+1)x(1+x)(1-x)
=x(1-x)
当x＝1＋√2时，原式＝(1＋√2)×[1－(1＋√2)]＝-√2(1+√2)=－√2－2.
括号打开 用x和（1+x²/（1-x²)）分别向除以（或者乘倒数）再用x²/（x+1）分别和（1+x²/（1-x²)）相除以（或者乘倒数）