莫一笔带过 小弟这道题实在不懂..
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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)