Stupid question, dealing with algebra and fractions.

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Discussion Overview

The discussion revolves around a participant's confusion regarding a specific algebraic manipulation in the context of solving a first-order ordinary differential equation (ODE). The focus is on the transition between two forms of the equation involving fractions and separation of variables, with an emphasis on the algebraic steps involved.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • A participant expresses difficulty in understanding the transition from dP/((P-5)*(P-2)) = -dt to (dP/3)*(1/(P-5) - 1/(P-2)) = -dt, specifically questioning the origin of the factor of 3.
  • Another participant suggests that the confusion can be resolved by using partial fraction decomposition, proposing that 1/[(P-2)(P-5)] can be expressed as A/(P-2) + B/(P-5) and encourages algebraic manipulation to find A and B.
  • Participants acknowledge the stress of finals and the commonality of making mistakes in foundational concepts, emphasizing that seeking clarification is important.

Areas of Agreement / Disagreement

Participants generally agree on the importance of clarifying foundational concepts, but the specific algebraic manipulation remains unresolved as the original poster has not confirmed understanding or acceptance of the proposed method.

Contextual Notes

The discussion highlights a potential gap in the participant's understanding of algebraic identities and manipulation, which may be affecting their ability to progress in solving the ODE.

Ryumast3r
Like the title says... I should be way past this (in ODEs+Lin. Algebra). I'm just really tired, have a final tomorrow, and cannot for the life of me understand why this works out the way it does.

Here goes (and please show most steps, it'd be greatly appreciated, thanks):

Start out with:

dP/dt = - (P-5)*(P-2)

Separate dP/dT since the whole point of this is to later integrate and solve an IVP, I get all that, just don't get the transition between this :

dP/((P-5)*(P-2)) = -dt and this next part here:

(dP/3)*(1/(P-5) - 1/(P-2)) = -dt

I know it's some fractions thing all from algebra that I should know, like I said, just cannot for the life of me figure it out, I get the whole "pull dP out" thing, it's where the 3 came from that I'm having trouble with. Tried to backsolve but I think there's just some identity I'm forgetting.

Anyway, any help would be greatly appreciated. Thanks. :)
 
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Ryumast3r said:
Like the title says... I should be way past this (in ODEs+Lin. Algebra). I'm just really tired, have a final tomorrow, and cannot for the life of me understand why this works out the way it does.

Here goes (and please show most steps, it'd be greatly appreciated, thanks):

Start out with:

dP/dt = - (P-5)*(P-2)

Separate dP/dT since the whole point of this is to later integrate and solve an IVP, I get all that, just don't get the transition between this :

dP/((P-5)*(P-2)) = -dt and this next part here:

(dP/3)*(1/(P-5) - 1/(P-2)) = -dt

I know it's some fractions thing all from algebra that I should know, like I said, just cannot for the life of me figure it out, I get the whole "pull dP out" thing, it's where the 3 came from that I'm having trouble with. Tried to backsolve but I think there's just some identity I'm forgetting.

Anyway, any help would be greatly appreciated. Thanks. :)

Hey there Ryumast3r and welcome to the forums.

Essentially what you are trying to do is turn 1/[(P-2) x (P-5)] into A/(P-2) + B/(P-5). You set both equal and do some algebra and you'll find that the P's cancel and you'll get numbers for A and B.
 
Right, thank you. :)

Sorry for the dumb question, I'm just so burnt out. :P

(also kinda embarrassed I had to ask that since I've gone through calc. :P)
 
Ryumast3r said:
Right, thank you. :)

Sorry for the dumb question, I'm just so burnt out. :P

(also kinda embarrassed I had to ask that since I've gone through calc. :P)

Dude don't stress, we all make simple mistakes. Its better to clarify things than to not clarify things and get more things wrong.
 
Yeah, thanks again.
 
^Lol, the reason it's "dumb" is because it's a fundamental part of the class I'm in and I totally forgot it. :P
 

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