the partial fraction decompostion of 44/(x^2-9) can be written in the form of f(x)/(x-3)+g(x)/(x+3) wheref(x)=_____g(x)=_____ **Partial Fraction Decomposition Overview**The partial fraction decomposition of the rational function \( \frac{44}{x^2 - 9} \) can be expressed in a simplified form. This decomposition allows us to break down the function into a sum of simpler fractions, making it easier to work with, especially in the context of integration or solving differential equations.The decomposition can be written in the form:\[ \frac{f(x)}{x - 3} + \frac{g(x)}{x + 3} \]In this expression, \( f(x) \) and \( g(x) \) are functions that we need to determine. The given rational function has a denominator, \( x^2 - 9 \), which can be factored as \( (x - 3)(x + 3) \). This factorization suggests that the partial fraction decomposition will involve the terms \( \frac{1}{x - 3} \) and \( \frac{1}{x + 3} \).To complete this decomposition, we need to find the specific forms of \( f(x) \) and \( g(x) \).\[ f(x) = \boxed{\phantom{x}} \]\[ g(x) = \boxed{\phantom{x}} \]Once \( f(x) \) and \( g(x) \) are determined, they can be substituted back into the decomposition to verify the correctness and to solve further mathematical problems involving the original rational function.

Name: the partial fraction decompostion of 44/(x^2-9) can be written in the
Uploaded: 2024-03-20T06:46:03.000Z
Channel: Bartleby
Description: the partial fraction decompostion of 44/(x^2-9) can be written in the form of f(x)/(x-3)+g(x)/(x+3) wheref(x)=_____g(x)=_____ **Partial Fraction Decomposition Overview**The partial fraction decomposition of the rational function \( \frac{44}{x^2 - 9}