<s>[INST] Given that $f(x) = 1 - 3/(x+2) + 3/(x+2)$ while $x ≠- 2$, show that $f(x) = (x^2 + x + 1)/(x+2)^2$ What type of problem is this and what are the first step(s) needed to tackle it?


Given that:
  $$f(x) = 1-\frac{3}{x + 2}+\frac{3}{(x  +2)^2}, \quad \text{with }x ≠ -2$$
  Show that:
  $$f(x) = \frac{x^2 + x +1}{(x + 2)^2}$$

It's fairly basic, clearly, but from my attempts so far it appears that finding common denominators doesn't take you from the first form to the second.
Should something be factorised?
 [/INST] No need of factorization, just evaluate the sum
$$1-\frac{3}{x + 2}+\frac{3}{(x  +2)^2}=\frac{(x  +2)^2-3(x  +2)+3}{(x  +2)^2}.$$
What do you obtain after expanding the numerator?
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