求y=(x^3-1)/(x^2-2x-3)的n阶导数
2个回答

分子3次,分母2次,且系数比是1,所以

原式=x+(Ax^2+Bx+C)/(x^2-2x-3)=(x^3 + (A-2)x^2 +(B-3)x +C)/(x^2-2x-3) 所以A=2,B=3,C=-1

所以原式=x+(Ax^2+Bx+C)/(x^2-2x-3)=x+(2x^2+3x-1)/(x^2-2x-3)

同理有原式=x+2+(7x+5)/(x^2-2x-3)=x+2+(7x+5)/(x+1)(x-3)