Question

(a^2-4a+4)/(a-1)-(3a^2+a-1)/(a+1)-(2a^2-5a-4)/(a-3)+(4a^2-18a-1)/(a-5)

提示：先部分分解，然后合理分组，部分分式时可以用长除法，也可以用十字相乘法

Answer 1

(a^2-4a+4)/(a-1)-(3a^2+a-1)/(a+1)-(2a^2-5a-4)/(a-3)+(4a^2-18a-1)/(a-5)
=(a-3)+1/(a-1)-(3a-2)-1/(a+1)-(2a+1)+1/(a-3)+(4a+2)+9/(a-5)
=1/(a-1)-1/(a+1)+1/(a-3)+9/(a-5)