The question has a linear factor in the denominator to the power of 3. I have only encountered 2 before. Have I started this question correctly? If I compare coefficients of x cubed the I find that A=2.
the method used in your picture is not correct, when you take x=-3, the denominator will become 0.
So you better to use comparing the coefficient when you encounter this kind of problem.
No, what he is doing is perfectly valid. (Except, of course, for the missing $\displaystyle \frac{1}{x+1}$ term.) Yes, the original form has a denominator of x+ 3 but after multiplying through by the least common denominator, he has a polynomial that is equal to that for all x other than those values that make the denominator 0. And since a polynomial is continuous, the value of the polynomial at 3 gives the correct value for the rational function as well.