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sara_87
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Homework Statement
we have 4/((s^2) + 4)(s-1)(s+3)
Homework Equations
The Attempt at a Solution
dividing it up do we get:
A/((s^2) + 4) + B/(s-1) + C/(s+3) = 4
or is it
(As + B)/((s^2) + 4) + C/(s-1) + D/(s+3) = 4
The purpose of using partial fractions in this equation is to simplify the expression and make it easier to solve. By breaking the fraction into smaller, simpler fractions, we can use algebraic methods to solve for the individual values of the variables.
To find the partial fraction decomposition of this equation, we first factor the denominator into its irreducible factors. Then, we set up a system of equations using the coefficients of each term in the numerator and equating them to the corresponding coefficients in the partial fraction decomposition. Finally, we solve for the unknown coefficients by using algebraic methods.
No, we can only use partial fractions to solve for the values of s that are not equal to the roots of the denominator. In this equation, the roots of the denominator are s=1 and s=-3, so we cannot use partial fractions to solve for these values of s.
The limitations of using partial fractions to solve this equation are that it only works for rational functions with a polynomial denominator and that it can only be used for values of s that are not equal to the roots of the denominator.
Yes, partial fractions can also be applied to other types of mathematical problems, such as integrals and differential equations. In these cases, the purpose is to break down a complex function into simpler fractions that can be integrated or differentiated more easily.