Partial Fraction of the Rational Expression:
x^2+x+8/x^3+x
x^3 + x = x(x^2 + 1)
So, you have
A/x + (Bx+C)/(x^2 + 1) = (x^2 + x + 8)/(x^3 + x)
Cross multiply and set coefficients equal to get
8/x + (1-7x)/(x^2+1)
x^2+x+8/x^3+x
So, you have
A/x + (Bx+C)/(x^2 + 1) = (x^2 + x + 8)/(x^3 + x)
Cross multiply and set coefficients equal to get
8/x + (1-7x)/(x^2+1)