QD Question 1 (Hao En)

1) Expansion of 2(2x^2+3) to make life easier for yourself (at least for me). Or you could choose not to. 

2) Since 4x^2+6 is a quadratic expression, the accompanying "unknowns" should be in linear form. Hence the Ax+B. As x-1 is linear, the unknown is a constant, giving us C. 

3) Multiplying both sides by the common denominator in order for us to be able to solve the question.

4) The substitution method is used here, as it is much more easier than the Comparing Coefficient method. As the expression on the left side is 5, at one glance it should be easy to tell that if we were to use the comparing coefficient method, solving the unknowns using simultaneous equations would be required. 

In this case, by substituting x=1, we are able to remove A and B from the equation, leaving us with only C.

5) Looking at the equation, as A is the only one with a x attached to it, we are able to tell that by substituting x=0 we would be able to remove the A. By removing A and using the answer for C we found out earlier, it would effectively leave us with only B. 

6) As A is the only one left, any value of x besides the ones that remove A from the equation will work. For simplicity's sake, -1 is used here.

7) Subbing back the unknowns into the partial fractions, and then simplifying them.

8) Rewriting of the answer to make life easier for Mr Johari.

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