Алгебра 8 класс учебник Макарычев, Миндюк ответы – номер 235

а) 5/y − 3 + 1/y + 3 − 4y − 18/y² − 9 = 5/y − 3 + 1/y + 3 − 4y − 18/(y − 3)(y + 3) = 5 ⋅ (y + 3)/(y − 3) ⋅ (y + 3) + 1 ⋅ (y − 3)/(y + 3) ⋅ (y − 3) − 4y − 18/(y − 3)(y + 3) = 5y + 15 + y − 3 − 4y + 18/(y − 3)(y + 3) = 2y + 30/(y − 3)(y + 3)
б) 2a/2a + 3 + 5/3 − 2a − 4a² + 9/4a² − 9 = 2a/2a + 3 − 5/2a − 3 − 4a² + 9/(2a − 3)(2a + 3) = 2a ⋅ (2a − 3)/(2a + 3) ⋅ (2a − 3) − 5 ⋅ (2a + 3)/(2a − 3) ⋅ (2a + 3) − 4a² + 9/(2a − 3)(2a + 3) = 4a² − 6a − 10a − 15 − 4a² − 9/(2a − 3)(2a + 3) = −16a − 24/(2a − 3)(2a + 3) = −8(2a − 3)/(2a − 3)(2a + 3) = −8(2a − 3) : (2a − 3)/(2a − 3)(2a + 3) : (2a − 3) = −8/2a + 3 = −8/2a + 3
в) 4m/4m² − 1 − 2m + 1/6m − 3 + 2m − 1/4m + 2 = 4m/(2m − 1)(2m + 1) − 2m + 1/3(2m − 1) + 2m − 1/2(2m + 1) = 4m ⋅ 6/(2m − 1)(2m + 1) ⋅ 6 − (2m + 1) ⋅ 2(2m + 1)/3(2m − 1) ⋅ (2m + 1) + (2m − 1) ⋅ 3(2m − 1)/2(2m + 1) ⋅ (2m − 1) = 24m − 2(2m + 1)² + 3(2m − 1)²/6(2m − 1)(2m + 1) = 24m − 8m² − 8m − 2 + 12m² − 12n + 3/6(2m − 1)(2m + 1) = 4m² + 4m + 1/6(2m − 1)(2m + 1) = (2m + 1)²/6(2m − 1)(2m + 1) = (2m + 1)² : (2m + 1)/6(2m − 1)(2m + 1) : (2m + 1) = 2m + 1/6(2m − 1)
г) 1/(x + y)² − 2/x² − y² + 1/(x − y)² = 1/(x + y)² − 2/(x − y)(x + y) + 1/(x − y)² = 1 ⋅ (x − y)²/(x + y)² ⋅ (x − y)² − 2 ⋅ (x − y)(x + y)/(x − y)(x + y) ⋅ (x − y)(x + y) + 1 ⋅ (x + y)²/(x − y)² ⋅ (x + y)² = x² − 2xy + y² − 2x² + 2y² + x² + 2xy + y²/(x + y)²(x − y)² = 4y²/(x + y)²(x − y)²
д) 4a² + 3a + 2/a³ − 1 − 1 − 2a/a² + a + 1 = 4a² + 3a + 2/(a − 1)(a² + a + 1) − 1 − 2a/a² + a + 1 = 4a² + 3a + 2/(a − 1)(a² + a + 1) − (1 − 2a) ⋅ (a − 1)/(a² + a + 1) ⋅ (a − 1) = 4a² + 3a + 2/(a − 1)(a² + a + 1) − (1 − 1 − 2a² + 2a)/(a² + a + 1) ⋅ (a − 1) = 4a² + 3a + 2/(a − 1)(a² + a + 1) − (3a − 1 − 2a²)/(a² + a + 1) ⋅ (a − 1) = 4a² + 3a + 2 − 3a + 2a²/(a − 1)(a² + a + 1) = 6a² + 3/(a − 1)(a² + a + 1) = 6a² + 3/a³ − 1
е) x − y/x² + xy + y² − 3xy/x³ − y³ + 1/x − y = x − y/x² + xy + y² − 3xy/(x − y)(x² + xy + y²) + 1/x − y = (x − y) ⋅ (x − y)/(x² + xy + y²) ⋅ (x − y) − 3xy/(x − y)(x² + xy + y²) + 1 ⋅ (x² + xy + y²)/(x − y) ⋅ (x² + xy + y²) = (x − y)² − 3xy + x² + xy + y²/(x − y)(x² + xy + y²) = x² − 2xy + y² − 3xy + x² + xy + y²/(x − y)(x² + xy + y²) = 2x² − 4xy + 2y²/(x − y)(x² + xy + y²) = 2(x² − 2xy + y²)/(x − y)(x² + xy + y²) = 2(x − y)²/(x − y)(x² + xy + y²) = 2(x − y)² : (x − y)/(x − y)(x² + xy + y²) : (x − y) = 2(x − y)/x² + xy + y²