SP #5: Unit J Concept 6: Partial Fraction Decomposition with Repeated Factors

In these first steps, the viewer must pay attention to the common denominator. The denominator must be the same for the entire function meaning, the viewer must foil the necessary functions to fit with the common denominator.

Next, the viewer must follow the foiling steps closely, for the tinniest mistake can lead to a wrong answer. After foiling, the next step is to combine the functions together under the common denominator, and equal it to the original function. From here we cancel out the denominators and combine like terms.

Once we have combined like terms,we solve for each variable. The viewer can choose to solve for the variables with ether elimination, or substitution. I chose elimination. Once you find your first value, you plug it in with another function, and solve for the next variable. Finally, with 2 values found, the viewer plugs in the values with the last variable and solves to find the last of the three values. Finally, we put the values into the A/(x-1)+ B/(x-2)+ C/(x-2)^2 function.

Finally, we compose the function to check if it is correct!