Partial Fraction Decomposition: Nominator or Denominator?

[myusernameis]

Homework Statement

do we look at the nominator or the denominator? are we trying to separate them? factoring them?

thanks

 

[tiny-tim]

Hi myusernameis!

do we look at the nominator or the denominator? are we trying to separate them? factoring them?

The denominator. And you factor it.

 

[myusernameis]

Hi myusernameis!


The denominator. And you factor it.

thanks for the answers!

so let's say i have this long equation in denom.

$$\frac{1}{(s^2+1)(s^2+4s-12)}$$

i can factor one of them to look like:

$$\frac{1}{(s^2+1)(s+6)(s-4)}$$

but then how do I know if I should use A +B or As+B, Cs+D, etc..?

 

[tiny-tim]

i can factor one of them to look like:

$$\frac{1}{(s^2+1)(s+6)(s-4)}$$

erm … nooo!

but then how do I know if I should use A +B or As+B, Cs+D, etc..?

sorry, not following you …

for a linear denominator, it's just a number on the top,

for a quadratic denominator, it's a linear top

 

[myusernameis]

erm … nooo!


sorry, not following you …

for a linear denominator, it's just a number on the top,

for a quadratic denominator, it's a linear top

haha made a mistake... so with that, do i use As+ B?

what if it's (s^2+2)(s^2+3)(s^2+5), ie, several s squares?

 

[myusernameis]

erm … nooo!


sorry, not following you …

for a linear denominator, it's just a number on the top,

for a quadratic denominator, it's a linear top

if was supposed to be a (s+6)(s-2)...

 

[tiny-tim]

what if it's (s^2+2)(s^2+3)(s^2+5), ie, several s squares?

each one has a linear top

if was supposed to be a (s+6)(s-2)...

each one has a number on the top

 

[myusernameis]

each one has a linear top

ok,

taking this example again: (s^2+2)(s^2+3)(s^2+5)

would it be: 1 = (As+B)/(s^2+2)(s^2+3)(s^2+5) + (Cs+D)/(s^2+2)(s^2+3)(s^2+5) + (Es+F)/(s^2+2)(s^2+3)(s^2+5) ?

 

[tiny-tim]

ok,

taking this example again: (s^2+2)(s^2+3)(s^2+5)

would it be: 1 = (As+B)/(s^2+2)(s^2+3)(s^2+5) + (Cs+D)/(s^2+2)(s^2+3)(s^2+5) + (Es+F)/(s^2+2)(s^2+3)(s^2+5) ?

uhh?

it's 1/(s²+2)(s²+3)(s²+5)

= (As+B)/(s²+2) + (Cs+D)/(s²+3) + (Es+F)/(s²+5)

 

[myusernameis]

uhh?

it's 1/(s²+2)(s²+3)(s²+5)

= (As+B)/(s²+2) + (Cs+D)/(s²+3) + (Es+F)/(s²+5)

haha brain fart on my part(i hope)


thanks

 

[tiny-tim]

haha brain fart on my part(i hope)

wow! where's your brain?

 

[myusernameis]

are you a math teacher?
if you don't mind me asking!

 

[tiny-tim]

i'm just a little goldfish …

trying to make sense of the bowliverse! ​

 

[myusernameis]

i'm just a little goldfish …

trying to make sense of the bowliverse! ​

haha! well, thanks for the help!