1. The numerator has a degree less than the denominator. (Tick)
2. The denominator can be factorised. (Tick)
Now, we require a partial fraction of the form
The numerator is always of one less degree than the denominator.
Getting the common denominator:
Can you see that since the denominators are equal, so must the numerators...
In this case, there does not exist an that you can use to eliminate the .
So we will use another method. Expand all the brackets...
Equating like powers of , we get
Can you see that for this equation to be true, then
Now you have three equations in three unknowns that you can solve simultaneously. Can you go from here?
But there does not exist any number that will be able to eliminate to find and .
Using your method...
Now that you have you should be able to solve the simultaneous equations I gave you easier.
But like I said, in this case, the ONLY method that will get you all three unknowns is to equate like powers of .
You substitute whatever will make the coefficients of A, B, C, etc = 0.
So in your case, we wanted the coefficient of to become 0.
So we let
Notice that the coefficient of A is . To try to eliminate A, we would need to let
Is it possible to square a number and end up with something negative?
You would only substitute if one of your coefficients happened to be .