How to factor $f''(x) = \frac{-12(x^2 + 3)^2 - (-48x(x^2 + 3)x)}{((x^2 + 3)^4))}$

Question

$$ f''(x) = \frac{-12(x^2 + 3)^2 - (-48x(x^2 + 3)x)}{((x^2 + 3)^4))} $$

The result is

$$ f''(x) = \frac {36(x+1)(x-1)}{(x^2+3)^3} $$

My try

$$ f''(x) = \frac{-12x^2 - 36 - (-48x(x^2 + 3)x)}{((x^2 + 3)^3))} $$

Answer 1

hint

the numerator can be written as

$$12 (x^2+3)\Bigl (-(x^2+3)+4x^2\Bigr) $$