Question

Partial Fraction Decomposition: I have everything right except the last linear.

Here's the given:
(x+4)/[(x^2)(x^2+4)]

Here is the system I got from it:
A+C=0
B+D=0
4A=1
4B=4

So when I solved for the first three unknowns, I got
A = 1/4
B = 1
C = -1/4

The back of the book says those are all correct, except for D, which gave me -1, but the book says it's x+4. How is that? Shouldn't it be x-1?

Answer 1

hmm D = -1 is correct
\[\frac{\frac{1}{4}x+1}{x^{2}} - \frac{\frac{1}{4}x+1}{x^{2}+4}\]
which simplifies to
\[\frac{1}{4}(\frac{x+4}{x^{2}} - \frac{x+4}{x^{2}+4})\]

Answer 2

Oops! I just figured it out. My answer is right, my book just wrote it differently *facepalm*
Instead of \[-\frac{ 1 }{ 12 }x - \frac{ 1 }{ 3 }\] which is my answer, it put it in unfactored form, which is
\[-\frac{ 1 }{ 12 }(x+4)\] which is the same thing, unless my tired brain is playing tricks on me...

Answer 3

Oops again, the above is actually for a different problem (gave me the same trouble though).

Answer 4

Please correct me if I'm wrong, but (and this is for the correct problem) here's my answer:
\[-\frac{ 1 }{ 4 }x - 1\]
and here's my book's answer:
\[-\frac{ 1 }{ 4 }(x+4)\]
They're the same thing, right?

Answer 5

yes same

Answer 6

I'll give you a medal just for the assurance you gave me :) Thank you!