11TH•Mathematics•Partial Fractions•Question 4

Solution

Resolve into partial fractions: $\dfrac{3x^2+3}{x^3+1}$

Factor:

x^3+1=(x+1)(x^2-x+1)

Let:

\frac{3x^2+3}{x^3+1}=\frac{A}{x+1}+\frac{Bx+C}{x^2-x+1}

Solving gives:

A=2,\quad B=1,\quad C=1

Hence:

\boxed{\frac{3x^2+3}{x^3+1}=\frac{2}{x+1}+\frac{x+1}{x^2-x+1}}

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