What is the correct form of the partial fraction decomposition for the expression the fraction with numerator 13 x minus 7 and denominator open paren x plus 2 close paren times open paren 4 x minus 3 close paren ?

The denominator factors into two distinct linear factors, (x + 2) and (4x − 3). For each distinct linear factor, the partial fraction decomposition uses a constant numerator over that factor. Thus the correct form is A/(x + 2) + B/(4x − 3), which is choice A.

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