Question

How do you write the partial fraction decomposition of the rational expression `8 / [ ( x + 2 ) ( x^2 + 4 ) ]`?

Answer 1

`1/(x+2) + (2-x)/ (x^2+4)`

Explanation:

Solve these three equations,

From 4A+2C=8 , A= `(2-C/2)`

From 2B+C=0, B= `-C/2`

Therefore, A+B=2-C=0, hence C=2, B=-1 and A= 1.

The partial fractions are therefore `1/(x+2) + (2-x)/ (x^2+4)`