解(1)：
x/(x-2)-3=a/(2-x)
x/(x-2)-a/(2-x)=3
x/(x-2)+a/(x-2)=3
(x+a)/(x-2)=3
3(x-2)=x+a
3x-6=x+a
3x-x=a+6
2x=a+6
x=(a+6)/2
當(dāng)x-2=0時(shí),方程有增根x=2
當(dāng)x=2時(shí)
(a+6)/2=2
a+6=4
a=-2
(2)：[(a²+1)/a]÷[(a²-1)/(a-1)]
=[(a²+1)/a]÷(a+1)
=(a²+1)/[a(a+1)]
=(a²+1)/(a²+a)
=[(-2)²+1]/[(-2)²+(-2)]
=5/2