# Thread: Expressing in partial fractions

1. ## Expressing in partial fractions

$(9x^2) / [(x -1)^2 * (x + 2)]$

It's part of a set of partial fractions I have to do.. I can't seem to solve this?

2. Originally Posted by erika
$(9x^2) / [(x -1)^2 * (x + 2)]$

It's part of a set of partial fractions I have to do.. I can't seem to solve this?
$\frac {9x^2}{(x - 1)^2 (x + 2)} = \frac {A}{x - 1} + \frac {B}{(x - 1)^2} + \frac {C}{x + 2}$

Can you take it from here?

3. Meh I did that and then tried substituting values for $x$ but it didn't seem to work

4. Originally Posted by erika
Meh I did that and then tried substituting values for $x$ but it didn't seem to work
Substitute values of x? do you know the method of partial fractions?

multiply through by the denominator of the left side, we get:

$9x^2 = A(x - 1)(x + 2) + B(x + 2) + C(x - 1)^2$

Can you take it from here? You can multiply out and equate coefficients, or you can choose convenient values of x that wipes out two variables at a time

5. sub x: 1
9 = 3B
3 = B

sub x: -1
36 = 9C
4 = C

By comparing coefficient of x^2:
9 = A + C
A = 5

Is that correct?

6. Originally Posted by erika

sub x: 1
9 = 3B
3 = B

sub x: -1
36 = 9C
4 = C

By comparing coefficient of x^2:
9 = A + C
A = 5

Is that correct?
Yes! Good Job!

7. Thank you!
One last question...

$
\frac {17x^2+23x+12}{(3x+4)(x^2+4)} = \frac{A}{3x+4} + \frac{B}{x^2+4}
$

By cover-up rule, I got
$
A = \frac {17(-4/3)^2+23(-4/3)+12}{(-4/3)^2+4}
= 2
$

But since $(x^2 +4)$ isn't linear, does it mean I follow the steps you mentioned earlier (multiply through by denominator, etc)?

8. Originally Posted by erika
Thank you!
One last question...

$
\frac {17x^2+23x+12}{(3x+4)(x^2+4)} = \frac{A}{3x+4} + \frac{B}{x^2+4}
$

By cover-up rule, I got
$
A = \frac {17(-4/3)^2+23(-4/3)+12}{(-4/3)^2+4}
= 2
$

what is this "cover-up" rule you are referring to?

But since $(x^2 +4)$ isn't linear, does it mean I follow the steps you mentioned earlier (multiply through by denominator, etc)?
yes, but you have to change the numerator. The numerator must always be one degree less than the denominator. so for the part where the denominator is $x^2 + 4$ you must write:

$\frac {Bx + C}{x^2 + 4}$