由x^2 -2x-3=0得：x=3或x=-1；
[(x^2-3)/(x-1)-2]÷[1/(x-1)]=[(x^2-3)/(x-1)-2](x-1)=x^2-3-2(x-1)=x^2-2x-1
当x=3时,x^2-2x-1=2；当x=-1时,x^2-2x-1=2,故：原式的值是2