Question

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(36a^2 5a2+13a-6 - 5a-2a+3 ) : 11a-2 a^2-2a-15 - 28a-a^22-5a

Answer 1

$( frac{36 {a}^{2} }{5 {a}^{2} + 13a - 6 } - frac{5a - 2}{a + 3} ) div frac{11a - 2}{ {a}^{2} - 2a - 15 } - frac{28a - {a}^{2} }{2 - 5a}$
Разложим 5a^2 + 13a - 6 на множители.
$d = {b}^{2} - 4ac = 169 - 4 times 5 times ( - 6) = 169 + 120 = 289 \ x1 = frac{ - 13 + 17}{2 times 5} = frac{4}{10} = frac{2}{5} \ x2 = frac{ - 13 - 17}{2 times 5} = frac{ - 30}{10} = - 3 \ 5 {x}^{2} + 13a - 6 = 5(a - frac{2}{5} )(a + 3) = (5a - 2)(a + 3)$
Разложим a^2 - 2a - 15 на множители:
$d = {b}^{2} - 4ac = 4 - 4 times ( - 15) = 64 \ a1 = frac{2 + 8}{2} = 5 \ a2 = frac{2 - 8}{2} = - 3 \ {a}^{2} - 2a - 15 = (a - 5)(a + 3)$
$( frac{36 {a}^{2} }{(5a - 2)(a + 3)} - frac{5a - 2}{a + 3} ) div frac{11a - 2}{(a - 5)(a + 3)} - frac{28 a - {a}^{2} }{2 - 5a} = frac{36 {a}^{2} - {(5a - 2)}^{2} }{(5a - 2)(a + 3)} div frac{11a - 2}{(a - 5)(a + 3)} - frac{28a - {a}^{2} }{ - (5a - 2)} = frac{(6a + 5a - 2)(6a - 5a + 2)}{(5a - 2)(a + 3)} times frac{(a - 5)(a + 3)}{11a - 2} + frac{28a - {a}^{2} }{5a - 2} = frac{(11a - 2)(a + 2)}{5a - 2} times frac{a - 5}{11a - 2} + frac{28a - {a}^{2} }{5a - 2} = frac{(a + 2)(a - 5)}{5a - 2} + frac{28a - {a}^{2} }{5a - 2} = frac{ {a}^{2} + 2a - 5a - 10 + 28a - {a}^{2} }{5a - 2} = frac{25a - 10}{5a - 2} = frac{5(5a - 2)}{5a - 2} = 5$