For the expression the fraction with numerator 9 x squared minus 8 and denominator open paren 3 x squared plus 4 close paren squared , which sum represents the correct form of the partial fraction decomposition?
Answer
A
the fraction with numerator cap A x plus cap b and denominator 3 x squared plus 4 plus the fraction with numerator cap c x plus cap d and denominator open paren 3 x squared plus 4 close paren squared
B
the fraction with numerator cap A and denominator 3 x squared plus 4 plus the fraction with numerator cap b and denominator open paren 3 x squared plus 4 close paren squared
C
the fraction with numerator cap A and denominator open paren 3 x squared plus 4 close paren squared plus the fraction with numerator cap b and denominator open paren 3 x squared plus 4 close paren squared
D
the fraction with numerator cap A x plus cap b and denominator open paren 3 x squared plus 4 close paren squared plus the fraction with numerator cap c x plus cap d and denominator open paren 3 x squared plus 4 close paren squared
Explanation
The denominator contains the repeated irreducible quadratic factor (3x² + 4)². For a repeated quadratic factor, include a linear numerator over each power: (Ax + B)/(3x² + 4) + (Cx + D)/(3x² + 4)². This matches choice A.
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