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# Partial Fractions watch

1. Firstly how could (x^2+1)/(x(x-1)) be re-written as 1+ (x+1)/(x(x-1))

and then how could (x+1)/(x(x-1)) be written as partial fractions. I'm guessing it would be something like A/(x)+ B/(x-1). Thanks for your help
2. For your first question, if you add and take away an x from the top of the equation (obviously having no overall effect) then you should be able to see that you can factorise a bit to obtain an x(x-1), which can be separated and cancelled to the 1+ that you require.

Secondly, you're right with the idea for A and B. Do this, multiply both sides by the bottom of your fraction and compare coefficients to get values for A and B

Hope this helps
3. For the first case: since the highest degree of x on the top is 2 and the highest degree of x on the bottom is also 2, its a good idea to long divide it first.
Thus :

After long dividing it, you're going to get this:

Then:

Now looks like :

4. (Original post by sunshinejessie)
For your first question, if you add and take away an x from the top of the equation (obviously having no overall effect) then you should be able to see that you can factorise a bit to obtain an x(x-1), which can be separated and cancelled to the 1+ that you require.

Secondly, you're right with the idea for A and B. Do this, multiply both sides by the bottom of your fraction and compare coefficients to get values for A and B

Hope this helps
So what you're saying is? You can re-write the top line as x^2+1+x-x then re-write it as x(x-1)+1+x. Then splitting it into two fractions you get x(x-1)/x(x-1) + x+1/x(x-1).

That then simplifies to 1+ (x+1)/x(x-1). I think

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