Question

Допоможіть будь ласка спростити вирази

Answer 1

Спростіть вираз

1)

$\frac{ {m}^{2} - mp }{ {m}^{2} + {p}^{2} } \times ( \frac{m}{m + p} + \frac{p}{m - p} ) = \frac{m(m - p)}{ {m}^{2} + {p}^{2} } \times \frac{m(m - p) + p(m + p)}{(m + p)(m - p)} = \frac{m(m - p)}{ {m}^{2} + {p}^{2} } \times \frac{ {m}^{2} - mp + mp + {p}^{2} }{(m + p)(m - p)} = \frac{m(m - p)( {m}^{2} + {p}^{2} ) }{( {m}^{2} + {p}^{2} )(m + p)(m - p) } = \frac{m \times 1 \times 1}{1 \times (m + p) \times 1} = \frac{m}{m + p}$

2)

$( \frac{5a + 1}{5a - 1} - \frac{5a - 1}{5a + 1} ) \div \frac{40 {a}^{2} }{5a - 1} = ( \frac{(5a + 1)(5a + 1) - (5a - 1)(5a - 1)}{(5a - 1)(5a + 1)} ) \times \frac{5a - 1}{40 {a}^{2} } = \frac{25 {a}^{2} + 5a + 5a + 1 - 25 {a}^{2} + 5a + 5a - 1}{(5a - 1)(5a + 1)} \times \frac{5a - 1}{40 {a}^{2} } = \frac{20a(5a - 1)}{(5a - 1)(5a + 1)40 {a}^{2} } = \frac{1 \times 1}{1 \times (5a + 1)2a} = \frac{1}{10 {a}^{2} + 2 a }$