Question

Calculus II Problem, Partial Fraction Decomposition.
I attached a file with my problem, its the last one.

Answer 1

O.o the paper is upside down

Answer 2

Yes I know, lol

Answer 3

http://www.wolframalpha.com/input/?i=expand+%28x^2%2B5x-9%29%2F%28%28x^2%2B1%29%28x%2B2%29%29

Answer 4

anyway, you've worked out most of the problem. Just use gaussian elimination

Answer 5

That link is for algebraically expanding, I need to use Partial Fraction Decomposition.

Answer 6

http://www.wolframalpha.com/input/?i=partial+fraction+decomposition+%28x^2%2B5x-9%29%2F%28%28x^2%2B1%29%28x%2B2%29%29

Answer 7

it even shows steps! :-D sorry about the first link...

Answer 8

The question is, how do they get that?

Answer 9

click on 'show steps' and substitute the thetas for A, B, and C

Answer 10

yeah, that's a matrix

Answer 11

There's an easier way than gaussian elimination; solving (perhaps using complex numbers).

Answer 12

oh the matrix is just gaussian elimination to solve for the A, B, and C

Answer 13

My answers should be
A=4
B=-3
C=-3
but from where I left off, where do I go from there?

Answer 14

From where you left off, just equate the coefficients on the left with the ones on the right:
\[x^2 +5x - 9 = (A+C)x^2 + (2A+B)x + (2B+C)\]
\[A+C = 1\]
\[2A+B = 5\]
\[2B+C = -9\]

Answer 15

After that, solve using gaussian elimination :-D

Answer 16

sorry if this seems stupid, but where do they get A+C=1 from?

Answer 17

A+C = 1 comes from equating the coefficient of \(x^2 \) on the left with the coefficient (A+B) of the \(x^2\) on the right

Answer 18

I see, I can't believe I missed that, :P

Answer 19

Thanks!

Answer 20

In case you haven't done elimination:

in the order A B C = constant, leaving out the variables:
1 0 1 1 <-- multiply this row by -2 and add to the 2nd row
2 1 0 5
0 2 1 -9

1 0 1 1 <-- multiply this row by -2 and add to the 2nd row
0 1 -2 3 (from adding -2 0 -2 -2 to 2 1 0 5)
0 2 1 -9

1 0 1 1
0 1 -2 3 <-- multiply this row by -2 and add to the 3rd row
0 2 1 -9

1 0 1 1
0 1 -2 3
0 0 5 -15 <--- means 5C= -15, C= -3

Backsubstitute C=-3 into the 2nd row to find B, and then finally B and C into the 1st row.