SP #4 Unit J Concept 5: Partial Fraction Decomposition

We are doing two things. We are solving backwards to get the original equation, and then decomposing it afterwards. In the below equation, let us get a common denominator. Multiply each factor by the value of the term that it does not have as a denominator. We then add like terms to get the "original equation" for our next step.

This is where the decomposing begins. Separate the equations as shown. Get a common denominator by doing the same thing we did before. Set the equation equal to the original one and add like terms. We will then get a system of 3 equations which we can plug into the matrix. Let us use rref and find A, B, and C and then we will plug in the values as its corresponding term which is the answer at the very bottom leftish.