- #1
myusernameis
- 56
- 0
Homework Statement
do we look at the nominator or the denominator? are we trying to separate them? factoring them?
thanks
myusernameis said:do we look at the nominator or the denominator? are we trying to separate them? factoring them?
tiny-tim said:Hi myusernameis!
The denominator. And you factor it.
myusernameis said:i can factor one of them to look like:
[tex]\frac{1}{(s^2+1)(s+6)(s-4)}[/tex]
but then how do I know if I should use A +B or As+B, Cs+D, etc..?
tiny-tim said: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
tiny-tim said: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
myusernameis said:what if it's (s^2+2)(s^2+3)(s^2+5), ie, several s squares?
myusernameis said:if was supposed to be a (s+6)(s-2)...
tiny-tim said:each one has a linear top
myusernameis said: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 said:uhh?
it's 1/(s2+2)(s2+3)(s2+5)
= (As+B)/(s2+2) + (Cs+D)/(s2+3) + (Es+F)/(s2+5)
myusernameis said:haha brain fart on my part(i hope)
tiny-tim said:i'm just a little goldfish …
trying to make sense of the bowliverse!
Partial fraction decomposition is used when you have a rational function, which is a fraction with polynomials in the numerator and denominator. It is used to break down the rational function into simpler fractions, making it easier to solve and integrate.
Partial fraction decomposition can simplify complex rational functions and make them easier to solve and integrate. It can also help identify and isolate specific terms within the fraction, making it easier to analyze and manipulate.
The process for partial fraction decomposition involves factoring the denominator of the rational function, setting up an equation with unknown coefficients for each distinct factor, and then solving for those coefficients using algebraic manipulation. The final result should be a sum of simpler fractions.
Partial fraction decomposition is not applicable when the denominator of the rational function cannot be factored or when the degree of the numerator is greater than or equal to the degree of the denominator. In these cases, other methods such as long division may be used to simplify the rational function.
Yes, partial fraction decomposition can also be used for improper rational functions, which are fractions where the degree of the numerator is greater than or equal to the degree of the denominator. The resulting partial fractions will include a polynomial term in addition to the simpler fractions.