(3a^2-15a+21)/(a^2-5a+6)-(2a^2-6a+1)/(a^2-3a+2)

用分离常数法，我们老师才讲过
(3a^2-15a+21)/(a^2-5a+6)-(2a^2-6a+1)/(a^2-3a+2)
=[3(a^2-5a+6)+3]/(a^2-5a+6)-[2(a^2-3a+2)-3]/(a^2-3a+2)
=3+3/(a^2-5a+6) -2+3/(a^2-3a+2)
=1+3[1/(a-2)(a-3)+1/(a-1)(a-2)]
=1-6/(a-1)(a-3)
=(a^2-4a-3)/(a-1)(a-3)
=(a^2-4a-3)/a^2-4a+3

可尝试用分离常数法
(3a^2-15a+21)/(a^2-5a+6)-(2a^2-6a+1)/(a^2-3a+2)
=[3(a^2-5a+6)+3]/(a^2-5a+6)-[2(a^2-3a+2)-3]/(a^2-3a+2)
=3+3/(a^2-5a+6) -2+3/(a^2-3a+2)
=1+3[1/(a-2)(a-3)+1/(a-1)(a-2)]
=1+6/(a-1)(a-3)
=(a^2-4a+9)/(a-1)(a-3)
=(a^2-4a+9)/a^2-4a+3

(3a^2-15a+21)/(a^2-5a+6)-(2a^2-6a+1)/(a^2-3a+2)
=(3a^2-15a+21)/(a-2)(a-3)-(2a^2-6a+1)/(a-2)(a-1)
=[(3a^2-15a+21)(a-1)-(2a^2-6a+1)(a-3)]/(a-1)(a-2)(a-3)
=[(3a^3-18a^2+36a-21)-(2a^3-12a^2+19a-3)]/(a-1)(a-2)(a-3)
=(a^3-6a^2+17a-18)/(a-1)(a-2)(a-3)
=(a-2)(a^2-4a+9)/(a-1)(a-2)(a-3)
=(a^2-4a+9)/(a-1)(a-3)