Find the partial fraction decomposition of the rational expression with prime quadratic factors in the denominator

When , you're left with



When or , you're left with



Adding the two equations together gives , or . Subtracting them gives , .

Now, you have





By just examining the leading and lagging (first and last) terms that would be obtained by expanding the right side, and matching these with the terms on the left side, you would see that and . These alone tell you that you must have and .

So the partial fraction decomposition is