Partial Fraction Decomposition - Help Please?

[knpoe03]

Hello!
In my PreCalc class, we are doing a partial fraction decomposition activity. I will link the work that I have so far in the space below. My teacher was absent during the week we learned this unit and instead we had to learn partial fraction decomposition from Youtube videos (which were not very helpful). Anyway, I am unsure if my work so far is correct, as I am unsure if I am doing things the right way.

In the top left corner, my initial addends are listed. Then, we must add and simplify these two addends. From this, we have to perform partial fraction decomposition to show how to get back to the original two addends. I used the Gauss-Jordan Elimination method to find A, B, and C. I'm not sure if this is correct, but I found this technique from awhile back in my math notes and I thought I'd give it a try. I thought I was almost done in getting back to the initial addends, but something just seems off. Can you please let me know where/if I have gone wrong or what I should be doing next?

I'd appreciate your help on this!

 

[pka]

Here is a link to what I think is the question: LOOK HERE
If need be please correct the post.

 

[Steven G]

Please post out your work. Many helpers here will not open an outside link.

 

[knpoe03]

Please post out your work. Many helpers here will not open an outside link.

Oh no! I'm fairly new, so let me look on how to do this and I will update it immediately.

 

[knpoe03]

 

[knpoe03]

Please post out your work. Many helpers here will not open an outside link.

I have just added photos of my work. Please let me know if you can view this.

 

[Dr.Peterson]

Since the fractions you started with have integer coefficients, the way to get back to the original is to factor the denominator only over the integers, namely as [MATH](x+2)(x^2+12x-2)[/MATH], and then find coefficients so that [MATH]\frac{-15x^2-341x+60}{(x+2)(x^2+12x-2)} = \frac{A}{x+2}+\frac{Bx+C}{x^2+12x-2}[/MATH]. The radicals make it harder, and overshoot the goal. I did it this way, and the work is not hard at all. But you have an arbitrary choice in combining the 16 with one of the fractions.

If the assignment was to choose your own pair of fractions to start with, you should start with proper fractions, to avoid that difficulty.

 

[knpoe03]

Since the fractions you started with have integer coefficients, the way to get back to the original is to factor the denominator only over the integers, namely as [MATH](x+2)(x^2+12x-2)[/MATH], and then find coefficients so that [MATH]\frac{-15x^2-341x+60}{(x+2)(x^2+12x-2)} = \frac{A}{x+2}+\frac{Bx+C}{x^2+12x-2}[/MATH]. The radicals make it harder, and overshoot the goal. I did it this way, and the work is not hard at all. But you have an arbitrary choice in combining the 16 with one of the fractions.

If the assignment was to choose your own pair of fractions to start with, you should start with proper fractions, to avoid that difficulty.

Thank you! Unfortunately, the assignment has us plug the dates of our birthday and month in a pre-defined equation. Trust me, if I could change it, I would!!