Question

Decompose -6x/(x-6)(x+3) into partial fractions.

Answer 1

What have you done so far?

Answer 2

Since they basically give you the answer in the problem.

Answer 3

I know x-6 and x+3 will be the denominators but I don't know how to get the numerator

Answer 4

A/(x-6)+B/(x+3), write on the same denominator. After you've written them on the same denominator, compare what you have and what you want.

Answer 5

-6x/[(x-6)(x+3)]=A/(x-6)+B/(x+3); as I said, write A and B on the same denominator, then you just compare with what you have and with what you need.

Answer 6

For example, you have no constants in the left-hand-side.

Answer 7

If there is a step you might not understand I'll explain it.

Answer 8

It's crucial for learning that you solve problems yourself though -- once you have seen someone elses solution to an example, then you are deprived, forever, of the benefit that could have come from trying it yourself.

Answer 9

\[\frac{-6x}{(x-6)(x+3)}=\frac{A}{x-6}+\frac{B}{x+3}\]
\[\frac{-6x}{(x-6)(x+3)}=\frac{Ax+3A+Bx-6B}{(x-6)(x+3)}=\frac{(A+B)x+3A-6B}{(x-6)(x+3)}\]Then
\[A+B=-6\\
3A-6B=0\Rightarrow A=-4, B=-2\]
\[\frac{-6x}{(x-6)(x+3)}=\frac{-4}{x-6}+\frac{-2}{x+3}\]
In case you still don't get the solution.

Answer 10

You should refrain from giving out answers John_ES, please read the Code of Conduct on Openstudy.

Answer 11

I was waiting for the feedback of @ejune420, but I think that it should be best if she can check her solution. Anyways, the question was closed so I think there was no problem. Sorry for the trouble.

Answer 12

I did not realize that the question had been closed; quite rude behavior from ejune420s part. Don't worry John_ES! :)

Answer 13

You were also right. It is better to help than provide the solution ;).

Answer 14

lol rude behavior on my part? gtfo. my internet went down and didn't come back up until today. And did I ask for anyone to give me an answer? no? Didn't think so. I posted the question to get help, no where did I say someone give me an answer. Good try tho :) @Noliec

Answer 15

I believe it. In my case, openstudy crash my explorer/firefox/chrome randomly. Sometimes I even has written an answer that has been deleted by the crash.

Answer 16

Yeah it crashes all the time on my google chrome. Thanks for not being an uppity jerk like that Noliec guy. You're awesome

Answer 17

Thanks, people should be more comprehensive with these problems that affect all of us.

Answer 18

How did you manage to close the question with no internet connection? ;)

Answer 19

I closed it once I got the answer, because I didn't need anyone else coming on helping, I already had you two on here to help me. That doesn't mean I was done coming to the question, I was trying to ask for an explanation when my internet went out. You've been a jerk from the start, so that's some rude behavior on your part. :)