Final answer:
The student's mathematics question involves calculating the partial fraction decomposition of (2x-9)/x(x+3) by assuming it equals A/x + B/(x+3), multiplying through by the common denominator, and solving for constants A and B.
Step-by-step explanation:
The student's question involves finding the partial fraction decomposition of the rational expression (2x - 9) / x(x + 3). To do this, we express the original fraction as a sum of simpler fractions whose denominators are the factors of the original denominator.
We assume that
(2x - 9) / x(x + 3) = A / x + B / (x + 3)
Multiplying both sides by the common denominator x(x + 3), we get
2x - 9 = A(x + 3) + Bx. Expanding and collecting like terms, we equate the coefficients of the corresponding powers of x on both sides to find A and B. This results in a system of linear equations which we solve to determine the values of A and B.
Once the values are found, we have the desired partial fraction decomposition, which can be used for further computations, such as integration or easier simplification.