Алгебра 8 класс учебник Макарычев, Миндюк ответы – номер 140

а) m² − 3m/8x² : 3m/8x = m² − 3m/8x² ⋅ 8x/3m = (m² − 3m) ⋅ 8x/8x² ⋅ 3m = m(m − 3) ⋅ 8x/8x² ⋅ 3m = m(m − 3) ⋅ 8x : 8x : m/8x² ⋅ 3m : 8x : m = m − 3/3x
б) 5a²/6b³ : a³/ab − b² = 5a²/6b³ ⋅ ab − b²/a³ = 5a² ⋅ (ab − b²)/6b³ ⋅ a³ = 5a² ⋅ b(a − b)/6b³ ⋅ a³ = 5a² ⋅ b(a − b) : a²b/6b³ ⋅ a³ : a²b = 5(a − b)/6ab²
в) x² + x³/11a² : 4 + 4x/a³ = x² + x³/11a² ⋅ a³/4 + 4x = (x² + x³) ⋅ a³/11a² ⋅ (4 + 4x) = x²(1 + x) ⋅ a³/11a² ⋅ 4(1 + x) = x²(1 + x) ⋅ a³ : (1 + x) ⋅ a²/11a² ⋅ 4(1 + x): (1 + x) ⋅ a² = ax²/44
г) 6ax/m² − 2m : 8ax/3m − 6 = 6ax/m² − 2m ⋅ 3m − 6/8ax = 6ax ⋅ (3m − 6)/(m² − 2m) ⋅ 8ax = 6ax ⋅ 3(m − 2)/m(m − 2) ⋅ 8ax = 6ax ⋅ 3(m − 2) : 2ax(m − 2)/m(m − 2) ⋅ 8ax : 2ax(m − 2) = 9/4m
д) a² − 3ab/3b : (7a − 21b) = a² − 3ab/3b ⋅ 1/7a − 21b = a(a − 3b) ⋅ 1/3b ⋅ 7(a − 3b) = a(a − 3b) : (a − 3b)/3b ⋅ 7(a − 3b) : (a − 3b) = a/21b
е) (x² − 4y²) : 5x − 10y/x = x² − (2y)²/1 ⋅ x/5x − 10y = (x − 2y)(x + 2y) ⋅ x/1 ⋅ 5(x − 2y) = (x − 2y)(x + 2y) ⋅ x : (x − 2y)/1 ⋅ 5(x − 2y) : (x − 2y) = x(x + 2y)/5
ж) (2ab − b)² : 4a³ − ab²/3 = (2ab − b)²/1 ⋅ 3/a((2a)² − b²) = (2ab − b)(2ab − b) ⋅ 3/1 ⋅ a(2a − b)(2a + b) = (2ab − b)(2ab − b) ⋅ 3 : (2a − b)/1 ⋅ a(2a − b)(2a + b) : (2a − b) = 3(2ab − b)/a(2a + b)
з) (10m − 15n) : (2m − 3n)²/2m = 10m − 15n/1 ⋅ 2m/(2m − 3n)² = 5(2m − 3n) ⋅ 2m/1 ⋅ (2m − 3n)(2m − 3n) = 5(2m − 3n) ⋅ 2m : (2m − 3n)/(2m − 3n)(2m − 3n) : (2m − 3n) = 10m/2m − 3n