How do you long divide (x-3)/(x^3+2x^2+x)x3x3+2x2+x?

1 Answer
Mar 29, 2017

-3/x +3/(x + 1) + 4/(x + 1)^23x+3x+1+4(x+1)2

Explanation:

I think you want partial fractions.
Factorize below: x(x^2 + 2x + 1) = x(x + 1)^2x(x2+2x+1)=x(x+1)2

frac{x-3}{x^3 + 2x^2 + x} = A/x +B/(x + 1) + C/(x + 1)^2x3x3+2x2+x=Ax+Bx+1+C(x+1)2
exists A,B,C in RR

x - 3 = A(x + 1)^2 +Bx(x+1) + Cx

x^2 : 0 = A + B
x^1: 1 = 2A + B + C
x^0: -3 = A Rightarrow B = +3

1 = 2(-3) + 3 + C Rightarrow C = 4