How do you express x^2/(x^2 + x +2)x2x2+x+2 in partial fractions?

1 Answer
Feb 15, 2016

Partial fractions of x^2/(x^2+x+2)x2x2+x+2 are 1-(x+2)/(x^2+x+21x+2x2+x+2

Explanation:

As the denominator x^2+x+2x2+x+2 is quadratic and its determinant (-b+-sqrt(b^2-4ac))/(2a)b±b24ac2a is not rational (as sqrt(b^2-4ac)=sqrt(-7)b24ac=7 is not rational), its partial fractions will be of type (Ax+B)/(x^2+x+2)Ax+Bx2+x+2.

But, degree of numerator is 22 hence let us write x^2/(x^2+x+2)x2x2+x+2 as

x^2/(x^2+x+2)=1-(x+2)/(x^2+x+2x2x2+x+2=1x+2x2+x+2

Hence partial fractions of x^2/(x^2+x+2)x2x2+x+2 are 1-(x+2)/(x^2+x+21x+2x2+x+2