Write the partial fraction decomposition of .

Multiply both sides by
x(x^{2}+2) [the lowest common denominator]

x^{2}+4x+6=A(x^{2}+2)+(Bx+C)x

x^{2}+4x+6=Ax^{2}+2A+Bx^{2}+Cx

x^{2}+4x+6=(A+B)x^{2}+Cx+2A

A=3, C=4

Substituting A=3 into the first equation à 3+B=1 à B=-2

So, the partial fraction decomposition is: