What is the partial fraction decomposition of the fraction with numerator 7 x squared minus 6 x plus 9 and denominator 3 x open paren 4 x squared plus 9 close paren ?

Combine the terms in choice A using the common denominator 3x(4x² + 9). The numerator becomes (4x² + 9) + 3x(x − 2) = 7x² − 6x + 9, which matches the original numerator. Therefore, the decomposition is 1/(3x) + (x − 2)/(4x² + 9), choice A.

AI-written and checked against the verified answer.