Question

What is the partial fraction decomposition?
Please help me. These are impossible. :(
-5x-15/(x+5)^2

Answer 1

You have a repeated linear factor in the denominator, so you decompose the fraction as such:\[\frac{-5x-15}{(x+5)^2}=\frac{A}{x+5}+\frac{B}{(x+5)^2}\]You then multiply both sides by (x+5)^2 to obtain\[-5x-15=A(x+5)+B\]Expand and collect like terms:\[-5x-15=Ax+(5A+B)\]In order for this to be true, we must have\[A=-5\](identifying it with the coefficient of x on the left) and \[5A+B=-15\]Since A has to be -5, we may solve for B:\[-15=5A+B=5(-5)+B=-25+B \rightarrow B=-15+25=10\]So A = -5 and B = 10, and your decomposition is\[\frac{-5x-15}{(x+5)^2}=-\frac{5}{x+5}+\frac{10}{(x+5)^2}\]

Answer 2

You can always check by cross-multiplying the right-hand side to see if it gets you back to what you had originally.

Answer 3

it's saying that's incorrect. :(

Answer 4

Sorry, Katie, but the answer is correct. I've double-checked. Maybe you've entered something wrong?

Answer 5

Ok, you're a genius. I forgot the negative. Please help me with 2 more problems?

Answer 6

Done.

Answer 7

partial decomposition of...
x^3+x^2-5/(x^2+7)^2

Answer 8

What is the partial fraction decomposition?
8x^2+20x+77/x(x-9)(x-8)

Answer 9

Last one please and thank you so much, but it's due in 8 minutes.

Answer 10

I can give you what I got, but I've rushed and can't guarantee.
\[\frac{77/72}{x}+\frac{60535/616}{x-9}-\frac{63299/693}{x-8}\]

Answer 11

wait

Answer 12

-749/8 for the x-8 one
905/9 for x-9 one
77/72 for x one

Answer 13

aw man too late

Answer 14

thank you so much for trying! you're awesome!

Answer 15

oh well...next time, don't leave it to the last minute! :p

Answer 16

Go to khanacademy.org or YouTube if you need to see how partial fraction decomposition is done :)

Answer 17

thank you!