Question

Помогите по математике 35(2), 39(6)

Answer 1

Ответ:

2)

$\frac{ {m}^{2} + 5m }{16 {m}^{2} - 1 } \div \frac{ {m}^{4} + 125m }{16 {m}^{2} - 8m + 1 } = \frac{m(m + 5)}{(4m - 1)(4m + 1)} \times \frac{ {(4 {m} - 1) }^{2} }{m( {m}^{3} + 125)} = \frac{m(m + 5)}{(4m - 1)(4m + 1)} \times \frac{ {(4m - 1)}^{2} }{m(m + 5)( {m}^{2} - 5m + 25) } = \frac{1}{4m + 1} \times \frac{4m - 1}{ {m}^{2} - 5m + 25 } = \frac{4m - 1}{(4m + 1)( {m}^{2} - 5m + 25)} = \frac{4m - 1}{4 {m}^{3} - 20 {m}^{2} + 100m + {m}^{2} - 5m + 25 } = \frac{4m - 1}{4 {m}^{3} - 19 {m}^{2} + 95m + 25 }$

6)

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