# Thread: [SOLVED] partial fraction decomposition

1. ## [SOLVED] partial fraction decomposition

i have to write the partial fraction decomposition of this and i really don't know how to begin.

x^2 - x / x^2 + x +1

2. Originally Posted by jbeybey
i have to write the partial fraction decomposition of this and i really don't know how to begin.

x^2 - x / x^2 + x +1
Start by noting that:

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

2. $x^2 + x + 1$ is an irreducible quadratic (what do you class notes or textbook say that you do in this case.....?)

3. Originally Posted by jbeybey
i have to write the partial fraction decomposition of this and i really don't know how to begin.

x^2 - x / x^2 + x +1
Since the numerator has the same degree as the denominator, the first thing will want to do is divide it out.
$\frac{x^2- x}{x^2+ x+ 1}= 1- \frac{2x+1}{x^2+ x+1}$

Since the denominator cannot be factored (by the quadratic formula it has no real roots), that is the "partial fraction decomposition".