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I would break this down into simple steps:

Step 1 - Equate the 2 expressions: (3 + 13x - 6x²) / (2x - 3) = Ax + B + C / (2x - 3)

Step 2 - Multiply both sides by the demoninator: 3...

The domain of the function allows us to write f(x)=x^x  as f(x)=e^{ln(x^x)}=e^{x ln(x)} (since ln(x) is defined on (0,oo) only). Using the standard derivati...

12x^2 +3

Step 1: Look at formula in formula booklet provided and write out formula.

Formula: (a+b)ⁿ= aⁿ+ ⁿc₁a^n-1b + ⁿC₂a^n-1<...

My first step would be to put all the known values on one side: ln(x) = ln(6) - ln(3) Then, using log laws, we have: ln(x) = ln(6/3) so, ln(x) = ln(2) so, x = 2