Question

What is the partial fraction decomposition of 7x squared- 6x +9/ 3x(4x squared +9)

Answer 1

9514 1404 393

Answer:

  1/(3x) =(x -2)/(4x^2 +9)

Step-by-step explanation:

The denominator cannot be factored further, so the final form will be ...

  A/(3x) + (Bx +C)/(4x^2 +9)

The value of this is ...

  (A(4x^2 +9) +(3x)(Bx +C))/(3x(4x^2 +9))

  = ((3B+4A)x^2 +3Cx +9A)/(3x(4x^2 +9))

Equating coefficients gives ...

  3B+4A = 7

  3C = -6   ⇒   C = -2

  9A = 9   ⇒   A = 1

Using the found value of A, we find ...

  3B +4 = 7   ⇒   B = 1

Then the decomposition is ...

  $\dfrac{7x^2-6x+9}{3x(4x^2+9)}=\boxed{\dfrac{1}{3x}+\dfrac{x-2}{4x^2+9}}$

Answer 2

Answer:

a

Step-by-step explanation:

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