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Partial Fractions Help

Express 1 t^2 / t^2(1 + t 2) in partial fractions.

So i got the whole A/t + B/t^2 + (Ct + D)/( t^2 + 1)

Put t=0 and got B= 1. Now how do I get A C and D? If I put t=3, I get 3 variables and I just don't know how to get those three.

Thanks
Reply 1
Original post by ChemBoy1
Express 1 t^2 / t^2(1 + t 2) in partial fractions.

So i got the whole A/t + B/t^2 + (Ct + D)/( t^2 + 1)

Put t=0 and got B= 1. Now how do I get A C and D? If I put t=3, I get 3 variables and I just don't know how to get those three.

Thanks

Can you please post the identity you're considering i.e. the line of working after A/t + B/t^2 + (Ct + D)/( t^2 + 1) ?
Original post by ChemBoy1
Express 1 t^2 / t^2(1 + t 2) in partial fractions.

So i got the whole A/t + B/t^2 + (Ct + D)/( t^2 + 1)

Put t=0 and got B= 1. Now how do I get A C and D? If I put t=3, I get 3 variables and I just don't know how to get those three.

Thanks

Put t=-1 and t=1 then solve a system of 3 eqs in 3 variables
Reply 3
Original post by RDKGames
Put t=-1 and t=1 then solve a system of 3 eqs in 3 variables

Comparing coefficients gets the answer quickly without the need for solving a system of equations.
Original post by Notnek
Comparing coefficients gets the answer quickly without the need for solving a system of equations.


So it does.
Didn’t look at it for long enough.
Is there not an easier way, it was only a 4 mark question, solving a 3 variable equation sees to much, is there not a simpler way?
Original post by RDKGames
Put t=-1 and t=1 then solve a system of 3 eqs in 3 variables
Reply 6
Original post by ChemBoy1
Is there not an easier way, it was only a 4 mark question, solving a 3 variable equation sees to much, is there not a simpler way?

Yes, comparing coefficients as I mentioned above. Try it and post your working if you get stuck.
Original post by ChemBoy1
Is there not an easier way, it was only a 4 mark question, solving a 3 variable equation sees to much, is there not a simpler way?


Compare coefficients as said above.

The simplest/quickest way to solve it is by saying:

1t2t2(1+t2)=(1+t2)2t2t2(1+t2)=(1+t2)t2(1+t2)2t2t2(1+t2)\dfrac{1-t^2}{t^2(1+t^2)} = \dfrac{(1+t^2) - 2t^2}{t^2(1+t^2)} = \dfrac{(1+t^2)}{t^2(1+t^2)}-\dfrac{2t^2}{t^2(1+t^2)}
...then cancel the common terms in both fractions to be left with the answer.
(edited 6 years ago)

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