Question

Помогите 20 балов пжжжжжжэ

Answer 1

▪1

$frac{{a}^{2} + {b}^{2} }{ {a}^{2} - {b}^{2} } - frac{a - b}{a + b} = frac{ {(a + b) }^{2} - 2ab - (a - b) ^{2} }{(a - b)(a + b)} = frac{ {a}^{2} + 2ab + {b}^{2} - 2ab - {a}^{2} + 2ab - {b}^{2} }{(a - b)(a + b)} = frac{2ab}{ {a}^{2} - {b}^{2} }$

▪2
$frac{3 {a}^{2} - 6 {a}^{2} }{ {a}^{2} - 9 } - frac{2a}{a - 3} = frac{ - 3 {a}^{2} - 2a(a + 3)}{ {a}^{2} - 9 } = frac{ - 3 {a}^{2} - 2 {a}^{2} - 6a }{ {a}^{2} - 9 } = frac{ - 5 {a}^{2} - 6a }{ {a}^{2} - 9 } = - frac{a(5a + 6)}{ {a}^{2} - 9 }$

▪3

$frac{2a}{ {a}^{2} - 9} - frac{1}{a + 3} = frac{2a - (a - 3)}{ {a}^{2} - 9} = frac{2a - a + 3}{{a}^{2} - 9} = frac{a + 3}{{a}^{2} - 9} = frac{1}{a - 3}$

▪4

$4c - frac{4 {c}^{2} - 2c}{2 + c} =frac{4c(2 + c) - 2c(2c - 1)}{2 + c} = frac{8c + 4 {c}^{2} - 4 {c}^{2} + 2c}{2 + c} = frac{10c}{2 + c}$

▪5

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

▪6

$frac{a + x}{a} div frac{ax + {x}^{2} }{ {a}^{2} } = frac{(a + x) times {a}^{2} }{a times x(a + x)} = frac{a}{x}$

▪7

$frac{a + 2}{ {a}^{2} } div frac{a + 2}{a - 3 {a}^{2} } = frac{(a + 2) times a(1 - 3a)}{ {a}^{2} times (a + 2)} = frac{1 - 3a}{a}$