Question

计算:1/(m²-m)+(m-2)/(2m²-2),并求当m=3时,原式的值

还有一题，
用两种不同的运算顺序计算
[x/（x-2）-x/（x+2）]×[(2-x)/x]
急啊，记住，先化简再求值

Answer 1

1/(m²-m)+(m-2)/(2m²-2)
=1/m(m-1)+(m-2)/2(m+1)(m-1)
=[2(m+1)+(m-2)m]/2m(m+1)(m-1)
=(2m+2+m²-2m)/2m(m+1)(m-1)
=(m²+2)/2m(m+1)(m-1)
m=3代入得
(9+2)/(2*3*4*2)
=11/48

先通分再算乘
[x/（x-2）-x/（x+2）]×[(2-x)/x]
=[x(x+2)-x(x-2)]/(x-2)(x+2)×[-(x-2)/x]
=-(x²+2x-x²+2x)/[(x+2)/x]
=-4x/[(x+2)/x]
=-4/(x+2)
直接用分配率
[x/（x-2）-x/（x+2）]×[(2-x)/x]
=x/(x-2)*[(2-x)/x]-x/(x+2)* (2-x)/x
=-1-(2-x)/(x+2)
=(-x-2+x-2)/(x+2)
=-4/(x+2)

Answer 2

将m=3代入
原式=1/6+1/16=11/48

追问

先化简再求值，你连化简都没花，直接带进去谁不会！

追答

1/(m²-m)+(m-2)/(2m²-2)=1/m(m­-1)+m-2/2(m+1)(m-1)=2(m+1)/2m(m+1)(m-1)+(m-2)m/2m(m+1)(m-1)=m²+2/2m(m²-1)
将m=3代入原式=1/6+1/16=11/48

追问

你的最后结果是m²+2/2m(m²-1)
可是你代代看,会是这个样子吗?
原式=1/6+1/16=11/48