hint. a fraction is negative (that is less than zero) if we divide a negative number by a positive number, and vice versa (obviously, division by 0 is a no-no).

the denominator of f'(x) is a perfect square, thus it is always greater than or equal to zero. so to find where f'(x) < 0, we simply solve for where the numerator is < 0

so you want to solve

you ended up doing this, but your mistake was this: if then