1. ## Partial Fractions

Write out the form of the partial fraction deconposition of the function. Do not determine the numerical values of the coefficients.
b. (x^2)/(x^2+x+2)

what i got was 1 - (x+2)/(x^2+x+2) and i don't have any A or B things in it so I dont know what i did wrong.. should it be 1- (Ax+B)/(x^2+x+2)??
is there a general formula that I missed?

2. you can't use partial fractions, because the denominator is irreducible on $\mathbb R.$

3. Originally Posted by Jasonium
Write out the form of the partial fraction deconposition of the function. Do not determine the numerical values of the coefficients.
b. (x^2)/(x^2+x+2)

what i got was 1 - (x+2)/(x^2+x+2) and i don't have any A or B things in it so I dont know what i did wrong.. should it be 1- (Ax+B)/(x^2+x+2)??
is there a general formula that I missed?
What you've done is as far as it can go.

4. $\frac{x^2}{x^2+x+2} = 1 - \frac{x-2}{x^2 + x + 2}$

We cannot factorize $x^2+x+2$ over $\mathbb{R}$, but we can over $\mathbb{C}$. So for some $A,B \in \mathbb{C}$,

$\frac{x-2}{x^2 + x + 2} \equiv \frac{A}{x-\alpha} + \frac{B}{x-\beta}$

Where $\alpha = \frac{-1-i\sqrt{7}}{2}$, $\beta = \frac{-1+i\sqrt{7}}{2}$