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

1 Answer
Jun 22, 2016

#1-(x+2)/(x^2+x+2).#

Explanation:

We note that the given Rational Fun. is Improper , because the Degree of Poly. in #Nr.=2# = the Degree of Poly. in #Dr.#

Also, the Poly. in #Dr.# can not be factorised, i.e., it is Irreducible.

To make it Proper, usually Long Division is preferred. But, we proceed as under :-

The Expression =#x^2/(x^2+x+2)={(x^2+x+2)-(x+2)}/(x^2+x+2)=(x^2+x+2)/(x^2+x+2)-(x+2)/(x^2+x+2)=1-(x+2)/(x^2+x+2).#

The desired expression in partial fraction is #1-(x+2)/(x^2+x+2).#