Verified answer

[tex] \frac{ {a}^{3} - 27}{ {a}^{2} + 3a + 9} = \frac{(a - 3)( {a}^{2} + 3a + 9) }{ {a}^{2} + 3a + 9 } = a - 3 [/tex]

[tex] \frac{16 - 8x + {x}^{2} }{ {(x - 4)}^{3} } = \frac{(4 - x)^{2} }{ {(x - 4)}^{3} } = \frac{ -(x - 4)^{2} }{(x - 4)^{3} } = - \frac{1}{x - 4} [/tex]