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katieb
 5 years ago
What is the partial fraction decomposition?
Please help me. These are impossible. :(
5x15/(x+5)^2
katieb
 5 years ago
What is the partial fraction decomposition? Please help me. These are impossible. :( 5x15/(x+5)^2

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0You have a repeated linear factor in the denominator, so you decompose the fraction as such:\[\frac{5x15}{(x+5)^2}=\frac{A}{x+5}+\frac{B}{(x+5)^2}\]You then multiply both sides by (x+5)^2 to obtain\[5x15=A(x+5)+B\]Expand and collect like terms:\[5x15=Ax+(5A+B)\]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\[\frac{5x15}{(x+5)^2}=\frac{5}{x+5}+\frac{10}{(x+5)^2}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0You can always check by crossmultiplying the righthand side to see if it gets you back to what you had originally.

KatieB
 5 years ago
Best ResponseYou've already chosen the best response.0it's saying that's incorrect. :(

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Sorry, Katie, but the answer is correct. I've doublechecked. Maybe you've entered something wrong?

KatieB
 5 years ago
Best ResponseYou've already chosen the best response.0Ok, you're a genius. I forgot the negative. Please help me with 2 more problems?

KatieB
 5 years ago
Best ResponseYou've already chosen the best response.0partial decomposition of... x^3+x^25/(x^2+7)^2

KatieB
 5 years ago
Best ResponseYou've already chosen the best response.0What is the partial fraction decomposition? 8x^2+20x+77/x(x9)(x8)

KatieB
 5 years ago
Best ResponseYou've already chosen the best response.0Last one please and thank you so much, but it's due in 8 minutes.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I can give you what I got, but I've rushed and can't guarantee. \[\frac{77/72}{x}+\frac{60535/616}{x9}\frac{63299/693}{x8}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0749/8 for the x8 one 905/9 for x9 one 77/72 for x one

KatieB
 5 years ago
Best ResponseYou've already chosen the best response.0thank you so much for trying! you're awesome!

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0oh well...next time, don't leave it to the last minute! :p

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Go to khanacademy.org or YouTube if you need to see how partial fraction decomposition is done :)
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