计算题：
[1/(m²-m)]+[(m-5)/(2m²-2)]
={ 1/[m(m-1)] }+{ (m-5)/[2(m+1)(m-1)] } 通分,最简公分母是2m(m+1)(m-1)
={ 2(m+1)/[2m(m+1)(m-1)] }+{ m(m-5)/[2m(m+1)(m-1)] }
=[2(m+1)+m(m-5)]/[2m(m+1)(m-1)]
=(2m+2+m²-5m)/[2m(m+1)(m-1)]
=(m²-3m+2)/[2m(m+1)(m-1)]
=(m-1)(m-2)/[2m(m+1)(m-1)]
=(m-2)/[2m(m+1)]
[a/(a-b)+b/(b-a)]÷[1/(a+b)]
=[a/(a-b)-b/(a-b)]×(a+b)
=[(a-b)/(a-b)]×(a+b)
=1×(a+b)
=a+b
解方程：
[1/(x+2)]+[1/(x-2)]=4/(x²-4) 方程两边同时乘最简公分母(x²-4)
x-2+x+2=4
2x=4
x=2
检验：把x=2代入x²-4=2²-4=4-4=0
经检验x=2是原方程的增根,原方程无解
[3x/(x+2)]+[2/(x-2)]=3 方程两边同时乘最简公分母(x+2)(x-2)
3x(x-2)+2(x+2)=3(x+2)(x-2)
3x²-6x+2x+4=3x²-12
-6x+2x=-12-4
-4x=-16
x=4
检验：把x=4代入(x+2)(x-2)=(4+2)(4-2)=12≠0
经检验x=4是原方程的根
(1-x)/(x-2)=[1/(2-x)]-2 方程两边同时乘最简公分母(x-2)
1-x=-1-2(x-2)
1-x=-1-2x+4
-x+2x=-1+4-1
x=2
检验：把x=2代入x-2=2-2=0
经检验x=2是原方程的增根,原方程无解
3/2-[1/(3x-1)]=5/(6x-2) 方程两边同时乘最简公分母2(3x-1)
3(3x-1)-2=5
9x-3-2=5
9x=5+3+2
9x=10
x=10/9
检验：把x=10/9代入2(3x-1)=2(3×10/9-1)=2×(10/3-1)=14/3≠0
经检验x=10/9是原方程的根