SP #4: Unit J Concept 5: Partial Fraction decomposition with distinct factors

Steps and Explanations!!

1. Compose the problem by multiplying the common denominator to each fraction (numerator).

2. Multiply the denominator to its common denominator also.

3. After multiplying the common denominator, write out the complete factors of the numerator and denominator.

4. Decompose the problem by rewriting the numerator and write the common denominator at the bottom.

5. To decompose, use letters A, B, and C. Find its common denominator and multiply.

6. Then set it equal to the previous answer that you found (the compose part).

7. Combine like terms to the appropriate number that you set equal to (ex. 9x^2 = something that has x^2).

8. Find the "system" by crossing out the x's.

9. Rewrite the system with the matrix format and plug it in to your graphing calculator. It should have the same answer that you started with in the problem.

       The viewer needs to pay attention to the common denominator since mistakes can easily be found when multiplied incorrectly. Make sure to know the difference between "compose" and "decompose". Matrix can help the viewer know if the answer is correct. Thus, it needs to match to what the problem started with.