Question

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

Answer 1

a

Explanation:

took test

Answer 2

9514 1404 393

Answer:

1/(3x) =(x -2)/(4x^2 +9)

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 ...

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