`(x^2 + x + 2)/(x^2 + 2)^2` Write the partial fraction decomposition of the rational expression.

`(x^2+x+2)/(x^2+2)^2`

Let`(x^2+x+2)/(x^2+2)^2=(Ax+B)/(x^2+2)+(Cx+D)/(x^2+2)^2`

`(x^2+x+2)/(x^2+2)^2=((Ax+B)(x^2+2)+Cx+D)/(x^2+2)^2`

`:.(x^2+x+2)=(Ax+B)(x^2+2)+Cx+D`

`x^2+x+2=Ax^3+2Ax+Bx^2+2B+Cx+D`

`x^2+x+2=Ax^3+Bx^2+(2A+C)x+2B+D`

Equating coefficients of like terms gives,

`A=0`

`B=1`

`2A+C=1`

`2B+D=2`

substituting the values of A and B in the above equations,

`2(0)+C=1`

`C=1`

`2(1)+D=2`

`2+D=2`

`D=2-2`

`D=0`

`:.(x^2+x+2)/(x^2+2)^2=1/(x^2+2)+x/(x^2+2)^2`