Question

Partial fractions: Write out the form of the partial fraction decomposition of the function. Do not determine the numerical values of the coefficients.

23. a. (2x) / ((x+3)(3x+1))

Answer 1

To perform a partial fraction decomposition for the function (2x) / ((x+3)(3x+1)), express the function as a sum of simpler fractions and solve for the unknown coefficients.

Step-by-step explanation:

To perform a partial fraction decomposition for the function (2x) / ((x+3)(3x+1)), we need to express the function as a sum of simpler fractions. The general form of a partial fraction decomposition of f(x) / g(x) is:
$$\frac{A}{x+3} + \frac{B}{3x+1}$$

where A and B are the unknown coefficients we need to determine. After finding the partial fraction decomposition, we can solve for the coefficients using various methods, such as the method of equating coefficients or the method of comparing coefficients.