Question

Write out the form of the partial fraction decomposition of the function (as in this example). Do not determine the numerical values of the coefficients. (a) x - 72/x² + x - 72 (b) 1/x² + x⁴ ______

Answer 1

To write the partial fraction decomposition of a function, factorize the denominator and express it as a sum of partial fractions.

Step-by-step explanation:

To write the partial fraction decomposition of the function, we need to factorize the denominator.

(a) For the function x - 72/x² + x - 72, we can factorize the denominator as (x - 8)(x + 9). Therefore, the partial fraction decomposition would be:

x - 72/(x - 8)(x + 9)

(b) For the function 1/x² + x⁴, the denominator is already factored. Therefore, the partial fraction decomposition would be:

1/x² + x⁴