Question

两道因式分解和化简求值题。

因式分解：(m+n)^2-(m-n)^2。

化简求值：〔（x^2-2x）/x-2〕÷x+（x^2-1）/（x^2-2x+1），其中

x＝1/2。

注：“/”为分数线。

速度噢～在线等，还有一定要有详细的解题过程，谢谢各位！o∩－∩o..
噢，抱歉。我漏掉了x-1是有加括号的.

Answer 1

(m+n)^2-(m-n)^2
=m^2+2mn+n^2-(m^2-2mn+n^2)
=2mn+2mn
=4mn

（（x^2-2x）/x-2〕÷x+（x^2-1）/（x^2-2x+1）
=(x-2-2)÷x+(x-1)(x+1)/(x-1)^2
=(x-4)÷x+（x+1)/(x-1)
因为x＝1/2，带入公式得：
=2(1/2-4)+(1/2+1)/(1/2-1)
=(1-8)+(3/2）/(-1/2)
=-7-3
=-10

若X-2是有括号的：
[（x^2-2x）/（x-2〕]÷x+（x^2-1）/（x^2-2x+1）
=[x(x-2)/(x-2)]÷x+(x-1)(x+1)/(x-1)^2
=1+（x+1)/(x-1)
因为x＝1/2，带入公式得：
=1+(1/2+1)/(1/2-1)
=1+(3/2）/(-1/2)
=1-3
=-2

Answer 2

(m+n)^2-(m-n)^2
=(m+n+m-n)(m+n-m+n)
=2m*2n
=4mn

〔（x^2-2x）/x-2〕÷x+（x^2-1）/（x^2-2x+1）
=((x^2-2x)/(x-2))*(1/x)+（x^2-1）/（x^2-2x+1）
=(x^2-2x)/(x^2-2x)+((x+1)(x-1))/(x-1)^2
=1+(x+1)/(x-1)
=1+1+2/(x-1)
=2+2/(x-1)
将x=1/2代入上式
=2+2/(1/2-1)
=-2

Answer 3

1.=（m+n+m-n）(m+n-m+n)=2m*2n=4mn

2.=1+(x+1)/(x-1)=1+(3/2)/(1/2-1)=-2