How do you express x^2/(x^2 + x +2) in partial fractions?

1 Answer
Feb 15, 2016

Partial fractions of x^2/(x^2+x+2) are 1-(x+2)/(x^2+x+2

Explanation:

As the denominator x^2+x+2 is quadratic and its determinant (-b+-sqrt(b^2-4ac))/(2a) is not rational (as sqrt(b^2-4ac)=sqrt(-7) is not rational), its partial fractions will be of type (Ax+B)/(x^2+x+2).

But, degree of numerator is 2 hence let us write x^2/(x^2+x+2) as

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

Hence partial fractions of x^2/(x^2+x+2) are 1-(x+2)/(x^2+x+2