Hi. In Calculus we are in a chapter about using partial fractions to find the integral. Maybe I've been up for too long, but I'm not sure how to decompose (correct verb?) this one:
$\displaystyle \frac{x^{2}-x}{x^{2}+x+1}$
Please advise.
Hi. In Calculus we are in a chapter about using partial fractions to find the integral. Maybe I've been up for too long, but I'm not sure how to decompose (correct verb?) this one:
$\displaystyle \frac{x^{2}-x}{x^{2}+x+1}$
Please advise.
Remember the steps for partial fractions. For the expression f(x)/g(x) first check the degree of polynomial in the numerator and denominator. The degree of numerator should be smaller than that of denominator if it is not the divide the numerator be the denominator and rewrite the expression. Now we will have f(x)/g(x) = p(x) + q(x)/g(x) where the degree of polynomial in numerator i.e., q(x) will be smaller than that in the denominator i.e., g(x).
Factorize g(x) and then proceed to write in partial fractions. If g(x) cannot be factorized then we just cannot do anything i.e., we cannot express it as partial fractions.