Verified answer

1)

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

2)

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

3)

[tex] \frac{ {m}^{2} }{ {(m - 5)}^{2} } - \frac{25}{ {(m - 5)}^{2} } = \frac{ {m}^{2} - 25 }{ {(m - 5)}^{2} } = \frac{(m - 5)(m + 5)}{ {(m - 5)}^{2} } = \frac{m + 5}{m - 5} [/tex]

4)

[tex] \frac{5x + 9}{ {x}^{2} - 1 } - \frac{4x + 8}{ {x}^{2} - 1 } = \frac{5x + 9 - 4x - 8}{ {x}^{2} - 1 } = \frac{x - 1}{ {x}^{2} - 1} = \frac{x - 1}{(x - 1)(x + 1)} = \frac{1}{x + 1} [/tex]