Алгебра 8 класс учебник Макарычев, Миндюк ответы – номер 82

а) x + 1/y = x ⋅ y/1 ⋅ y + 1/y = xy + 1/y
б) 1/a − a = 1/a − a ⋅ a/1 ⋅ a = 1 − a²/a
в) 3a − a/4 = 3a ⋅ 4/1 ⋅ 4 − a/4 = 12a − a/4 = 11a/4
г) 5b − 2/b = 5b ⋅ b/1 ⋅ b − 2/b = 5b² − 2/b
д) a² + b/a − a = a² + b/a − a ⋅ a/1 ⋅ a = a² + b − a²/a = b/a
е) 2p − 4p² + 1/2p = 2p ⋅ 2p/1 ⋅ 2p − 4p² + 1/2p = 4p² − 4p² − 1/2p = −1/2p = −1/2p
ж) (a − b)²/2a + b = (a − b)²/2a + b ⋅ 2a/1 ⋅ 2a = (a − b)² + 2ab/2a = a² − 2ab + b² + 2ab/2a = a² + b²/2a
з) c − (b + c)²/2b = c ⋅ 2b/1 ⋅ 2b − (b + c)²/2b = 2cb − (b + c)²/2b = 2cb − (b² + 2bc + c²)/2b = 2cb − b² − 2bc − c²/2b = −b² − c²/2b = b² + c²/2b