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partial fractions - help needed

Here is the question I am doing:

lappar.JPG

Here are my calculations so far:

IMG_1524.JPG

I know I am going wrong somewhere but I don't know where. When solving the last two equations (shown) simultaneously I am getting different answers for C.

Any help on this is hugely appreciated thank you!
Reply 1
Avatar for davros
davros
16
Original post by Kaya_01
Here is the question I am doing:

lappar.JPG

Here are my calculations so far:

IMG_1524.JPG

I know I am going wrong somewhere but I don't know where. When solving the last two equations (shown) simultaneously I am getting different answers for C.

Any help on this is hugely appreciated thank you!


Because s2+1s^2 + 1 is a quadratic factor, it needs a numerator like Bs + C. If you think about it, there's no point in having one term with numerator B and another with numerator C over the same factor, because you could just combine them into one constant D = B + C :smile:
Original post by Kaya_01
Here is the question I am doing:

lappar.JPG

Here are my calculations so far:

IMG_1524.JPG

I know I am going wrong somewhere but I don't know where. When solving the last two equations (shown) simultaneously I am getting different answers for C.

Any help on this is hugely appreciated thank you!


Just split the first term into two separate fractions.
which should give you 1S2−1S2+1 \frac{1}{S^2}-\frac{1}{S^2+1} Then separate the s−2s2+1 \frac{s-2}{s^2+1} into ss2+1−2s2+1\frac{s}{s^2+1}-\frac{2}{s^2+1} you should then be able to see how to get the required result.
Reply 3
Avatar for Kaya_01
Kaya_01
OP
11
Original post by davros
Because s2+1s^2 + 1 is a quadratic factor, it needs a numerator like Bs + C. If you think about it, there's no point in having one term with numerator B and another with numerator C over the same factor, because you could just combine them into one constant D = B + C :smile:



would I then equate it to A/s^2 + Bs+c/(s^2+1) ? What about the third denominator and what about the LHS?

thank you
Reply 4
Avatar for joostan
joostan
13
Original post by Kaya_01
would I then equate it to A/s^2 + Bs+c/(s^2+1) ? What about the third denominator and what about the LHS?

thank you


The only term which requires partial fractions is the: 1s2(s2+1)\dfrac{1}{s^2(s^2+1)}
So let:
1s2(s2+1)=As+Bs2+Cs+Ds2+1\dfrac{1}{s^2(s^2+1)}=\dfrac{A}{s}+\dfrac{B}{s^2}+\dfrac{Cs+D}{s^2+1}
The s−2s2+1\dfrac{s-2}{s^2+1} in the LHS can be accounted for after your partial fractions. :smile:
Reply 5
Avatar for davros
davros
16
Original post by Kaya_01
would I then equate it to A/s^2 + Bs+c/(s^2+1) ? What about the third denominator and what about the LHS?

thank you


There isn't a "third" denominator - if you look at what they've done, they've just split out the bit over (s^2 + 1) into 2 separate fractions!

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