A community for students.
Here's the question you clicked on:
 0 viewing
UnkleRhaukus
 3 years ago
PartialFraction Decomposition
\[\frac1{p^2(p^24)}\]
UnkleRhaukus
 3 years ago
PartialFraction Decomposition \[\frac1{p^2(p^24)}\]

This Question is Closed

UnkleRhaukus
 3 years ago
Best ResponseYou've already chosen the best response.1\[\begin{align*}\frac1{p^2(p^24)}&=\frac1{p^2(p+2)(p2)}\\ \\&=\frac Ap+\frac B{p^2}+\frac C{p+2}+\frac D{p2}\\ \\\end{align*}\]

UnkleRhaukus
 3 years ago
Best ResponseYou've already chosen the best response.1\[1=Ap(p+2)(p2)+B(p+2)(p2)+Cp^2(p2)+Dp^2(p+2)\]

Yahoo!
 3 years ago
Best ResponseYou've already chosen the best response.0Put Values for p and Find A , B , C D

Yahoo!
 3 years ago
Best ResponseYou've already chosen the best response.01st put P = 2 and Find D

UnkleRhaukus
 3 years ago
Best ResponseYou've already chosen the best response.1\[1=Ap(p+2)(p2)+B(p+2)(p2)+Cp^2(p2)+Dp^2(p+2)\] \[\text{for }p=0\\\qquad1=4B\]\[\qquad B=\frac{1}4\] \[\text{for }p=2\]\[\qquad1=16D\]\[\qquad D=\frac 1{16}\] \[\text{for }p=2\]\[\qquad1=16C\]\[\qquad C=\frac {1}{16}\] \[\text{for }p=1\]\[\qquad1=3A+3BC+3D\] \[\qquad1=3A\frac34+\frac 1{16}+\frac3{16}\]\[\qquad1=3A\frac34+\frac 4{16}\]\[\qquad\frac32=3A\]\[\qquad A=\frac{1}{2}\] \[\frac1{p^2(p^24)}=\frac 1{2p}\frac 1{4p^2}\frac 1{16(p+2)}+\frac 1{16(p2)}\]

UnkleRhaukus
 3 years ago
Best ResponseYou've already chosen the best response.1i think \(A\) is ment to be zero , , can you see my mistake ?

UnkleRhaukus
 3 years ago
Best ResponseYou've already chosen the best response.1found it / (them)\[\begin{align*}\text{for }p=1&&1&=3A3BC+3D\\ &&1&=3A+\frac34+\frac 1{16}+\frac3{16}\\ &&1&=3A+1\\ \\ &&A&=0\\ \end{align*}\]

UnkleRhaukus
 3 years ago
Best ResponseYou've already chosen the best response.1\[F(p)=\frac1{p^2(p^24)}=\frac 1{4p^2}\frac 1{16(p+2)}+\frac 1{16(p2)}\]
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.