Question

Упростите выражение.
Варианты ответов
2a
a+1
1
1/a-8

Answer 1

$( \frac{1}{ {(a - 2)}^{2} } + \frac{2}{ {a}^{2} - 4 } + \frac{1}{ {(a + 2)}^{2} } ) \div \frac{2a}{ {( {a}^{2} - 4) }^{2} } =$

$= ( \frac{1}{ (a - 2)(a - 2) } + \frac{2}{ (a - 2)(a + 2)} + \frac{1}{ (a + 2)(a + 2)} ) \times \frac{ {((a - 2)(a + 2))}^{2} }{ 2a } =$

$= \frac{ {(a + 2)}^{2} +2(a - 2)(a + 2)+ {(a - 2)}^{2}}{ ((a - 2)(a + 2))^{2}} \times \frac{ {((a - 2)(a + 2))}^{2} }{ 2a } =$

$= \frac{ {a}^{2} + 4a + 4 +2 {a} - 8+ {a}^{2} - 4a + 4 }{ 1} \times \frac{ 1}{ 2a } =$

$= \frac{2 {a}^{2} + 2a }{2a} = \frac{2a \times (a + 1)}{2a} = a + 1$