Answer:
[tex]\dfrac{A}{x}+\dfrac{B}{x-6}[/tex]
Step-by-step explanation:
Given the function [tex]\dfrac{37}{x(x-6)}[/tex], to write the form of its partial fraction on decomposition, we will separate the two functions separated by an addition sign. The numerator of each function will be constants A and b and the denominator will be the individual factors of each function at the denominator. The partial fraction of the rational function is as shown below.
[tex]= \dfrac{37}{x(x-6)}\\\\= \dfrac{A}{x}+\dfrac{B}{x-6}[/tex]
Since we are not to solve for the constants, hence the partial fraction is [tex]\dfrac{A}{x}+\dfrac{B}{x-6}[/tex]
