1. ## Partial Fractions

Hello, Thanks in advance for any help with this question.

I am fairly comfortable with these, however the minus on the numerator is throwing me off!

Question) Express as the sum of partial fractions:

-3 / (2x+1)(x-3)

Usually I would say A / (2x+1) + B / (x-3)

So that -3 = A(x -3) + B(2x+1) and then sub x = 3 so that A=0

Giving -3 = 0 + 7B

But that means B is a a complicated decimal!! -3/7 = -0.42857 which is no good!

Thanks again for any assitance.

Mike

2. Originally Posted by mikewhant
Hello, Thanks in advance for any help with this question.

I am fairly comfortable with these, however the minus on the numerator is throwing me off!

Question) Express as the sum of partial fractions:

-3 / (2x+1)(x-3)

Usually I would say A / (2x+1) + B / (x-3)

So that -3 = A(x -3) + B(2x+1) and then sub x = 3 so that A=0

Giving -3 = 0 + 7B

But that means B is a a complicated decimal!! -3/7 = -0.42857 which is no good!

Thanks again for any assitance.

Mike
I've not had chance to look through & see if you calculations are correct, but you are overcomplicating the issue.

Take the fraction $\frac{a}{3}$ for example. If $a=8$, then the fraction would be $\frac{8}{3}$, simple enough.

If however, $a=\frac{1}{2}$, then you would get $\frac{\frac{1}{2}}{3}$, which is 1, divided by 2, divided by 3.

Therefore you can write this as $\frac{1}{6}$.

Therefore in your above question, you have $\frac{\frac{-3}{7}}{x-3}$, using the rules above this would give you...

3. you can "throw" the negative sign from numerator into either the (2x + 1) or the (x - 3) of the denominator. for example -(x - 3) = 3 - x

$-\frac{3}{(2x + 1)(x - 3)} = \frac{3}{(2x + 1)(3 - x)}$

let $\frac{3}{(2x + 1)(3 - x)} = \frac{A}{2x + 1} + \frac{B}{3 - x}$

Hence, 3 = A(3 - x) + B(2x + 1)
0x + 3 = (2B - A)x + (3A + B)
2B - A = 0
A = 2B ...(1)
3A + B = 3 ...(2)
Solving these equation you get A = $\frac{3}{7}$, B = $\frac{6}{7}$

so $-\frac{3}{(2x + 1)(x - 3)}$ = $\frac{6}{7(2x + 1)} + \frac{3}{7(3 - x)}$
or = $\frac{6}{7(2x + 1)} - \frac{3}{7(x - 3)}$

4. excellent, thanks to both of you, i've got it now!