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Core 4 splitting partial fractions help!! :)

the question asked me to show (2 / (x - 1) (x - 3)) in partial fractions which i did and got : (1 / (x - 3)) - (1 / (x - 1)) which is correct

it then asked to use that answer to express (4 / ((x - 3)^2)((x - 1)^2)) in partial fractions,
i thought i would just have to add a (1 / (x - 1)^2) and (1 / (x - 3)^2), which would give: (1 / (x - 3)) + (1 / (x - 3)^2) - (1 / (x - 1)) + (1 / (x - 1)^2),

but the answer in the back is very slightly different:
(1 / (x - 3)) - (1 / (x - 3)^2) + (1 / (x - 1)) + (1 / (x - 1)^2)

can someone explain why i am wrong and explain a method?
or is the book is wrong

thanks in advance :biggrin:
(edited 13 years ago)
Reply 1
anyone? :s-smilie:
Original post by goerigi
it then asked to use that answer to express (4 / ((x - 2)^2)((x - 1)^2)) in partial fractions,


you sure that bit is correct?
Reply 3
Original post by Freakonomics123
you sure that bit is correct?


ohh that should be (x - 3)^2. typo! sorry
Reply 4
Original post by Freakonomics123
you sure that bit is correct?


so do you have any ideas :smile:
Reply 5
(4 / ((x - 3)^2)((x - 1)^2))

equals the square of

(2 / (x - 1) (x - 3)) = square of [(1 / (x - 3)) - (1 / (x - 1))]
Reply 6
Original post by vc94
(4 / ((x - 3)^2)((x - 1)^2))

equals the square of

(2 / (x - 1) (x - 3)) = square of [(1 / (x - 3)) - (1 / (x - 1))]


thanks :smile: but could you explain how (2 / (x - 1) (x - 3)) = square of [(1 / (x - 3)) - (1 / (x - 1))
Reply 7
Original post by goerigi
thanks :smile: but could you explain how (2 / (x - 1) (x - 3)) = square of [(1 / (x - 3)) - (1 / (x - 1))


the square of 2(x2)(x3)=\frac{2}{(x-2)(x-3)} = the square of 1(x3)1(x1)\frac{1}{(x-3)} - \frac{1}{(x-1)}

because;

2(x2)(x3)=1(x3)1(x1)\frac{2}{(x-2)(x-3)} = \frac{1}{(x-3)} - \frac{1}{(x-1)}

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