Question

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Answer 1

$a) \frac{ {a}^{2} - 16 }{8 + 2a} = \frac{ {a}^{2} - {2}^{4} }{2a + 8} = \frac{ {a}^{2} - { {(2}^{2}) }^{2} }{2a + {2}^{3} } = \frac{ {(a - 2}^{2})(a + {2}^{2}) }{2( \frac{2a}{2} + \frac{ {2}^{3} }{2}) } = \frac{(a - 4)(a + 4)}{2(a + {2}^{3 - 1}) } = \frac{(a - 4)(a + 4)}{2(a + {2}^{2}) } = \frac{(a - 4)(a + 4)}{2(a + 4)} = \frac{a - 4}{2}$

$b) \frac{ {a}^{2} + 6a + 9 }{5a + 15} = \frac{ {a}^{2} + 2a \times 3 + {3}^{2} }{5a + 3 \times 5} = \frac{ {(a + 3)}^{2} }{5( \frac{5a}{5} + \frac{3 \times 5}{5}) } = \frac{ {(a + 3)}^{2} }{5(a + 3) } = \frac{ {(a + 3)}^{2 - 1} }{5} = \frac{a + 3}{5}$