Алгебра 8 класс учебник Макарычев, Миндюк ответы – номер 150

а) (x/y² − 1/x) : (1/y + 1/x) = (x ⋅ x/y² ⋅ x − 1 ⋅ y²/x ⋅ y²) : (1 ⋅ x/y ⋅ x + 1 ⋅ y/x ⋅ y) = (x²/xy² − y²/xy²) : (x/xy + y/xy) = (x² − y²/xy²) : (x + y/xy) = x² − y²/xy² ⋅ xy/x + y = (x − y)(x + y) ⋅ xy/xy² ⋅ (x + y) = (x − y)(x + y) ⋅ xy : (x + y) ⋅ xy/xy² ⋅ (x + y) (x + y) ⋅ xy = x − y/y
б) (a/m² + a²/m³) : (m²/a² + m/a) = (a ⋅ m/m² ⋅ m + a²/m³) : (m²/a² + m ⋅ a/a ⋅ a) = (am + a²/m³) : (m² + am/a²) = am + a²/m³ ⋅ a²/m² + am = a(m + a)/m³ ⋅ a²/m(m + a) = a(m + a) ⋅ a²/m³ ⋅ m(m + a) = a(m + a) ⋅ a² : (m + a)/m³ ⋅ m(m + a) : (m + a) = a³/m⁴
в) ab + b²/3 : b³/3a + a + b/b = b(a + b)/3 ⋅ 3a/b³ + a + b/b = b(a + b) ⋅ 3a/3 ⋅ b³ + a + b/b = b(a + b) ⋅ 3a : 3b/3 ⋅ b³ : 3b + a + b/b
г) x − y/x − 5y/x² ⋅ x² − xy/5y = x − y/x − 5y ⋅ x(x − y)/x² ⋅ 5y = x − y/x − 5y ⋅ x(x − y) : 5xy/x² ⋅ 5y : 5xy = x − y/x − (x − y)/x = x − y − x + y/x = 0/x = 0