Stupid question, dealing with algebra and fractions.

[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. :)

 

[chiro]

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.

 

[Ryumast3r]

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)

 

[chiro]

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.

 

[Ryumast3r]

Yeah, thanks again.

 

[Ryumast3r]

^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