(x-1)/(x^2-5x+6)=a/(x-2)+b/(x-3)=[a(x-3)+b(x-2)]/(x^2-5x+6)
所以x-1=ax-3a+bx-2b=(a+b)x-(3a+2b)
所以a+b=1,-（3a+2b）=-1
a=-1,b=2