partial fraction expansion of x2x2x1Solutionthe question ask

partial fraction expansion of (x+2)/(x^2+x+1)

Solution

the question asks us to find the partial fraction expansion of the given rational function

the rational function should satisfy two conditions before doing the prtial fraction expansion

firstly the degree of numerator should be less that degree of denominator , which is satisfied in our question as degree of numerator is 1 and degree of denom is 2

secondly the denom should be factorable

x^2+x+1 cant be factored thus we cant find the partial fraction expansion , the only expansion it can follow is separating it into two terms

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

so the given rational function doesnt have the partial fraction expansion