Алгебра 8 класс учебник Макарычев, Миндюк ответы – номер 155

а) (a² + 2a + 1) ⋅ (1/a + 1 + 1/a² − 1 − 1/a − 1)
1) (1 ⋅ (a − 1)/(a + 1) ⋅ (a − 1) + 1/(a − 1) ⋅ (a + 1) − 1 ⋅ (a + 1)/(a − 1) ⋅ (a + 1)) = (a − 1 + 1 − a − 1/(a + 1) ⋅ (a − 1)) = (−1/(a + 1) ⋅ (a − 1))
2) (a² + 2a + 1) ⋅ (−1/(a + 1) ⋅ (a − 1)) = (a + 1)²/1 ⋅ (−1/(a + 1) ⋅ (a − 1)) = (a + 1)(a + 1) ⋅ (−1)/1 ⋅ (a + 1) ⋅ (a − 1) = (a + 1)(a + 1) ⋅ (−1) : (a + 1)/1 ⋅ (a + 1) ⋅ (a − 1) : (a + 1) = −(a + 1)/a − 1 = −a + 1/a − 1 = a + 1/1 + a
б) (1 − 9x² + 4/12x) : (1/3x − 1/2) + 1
1) (1 − 9x² + 4/12x) = 12x/12x − 9x² + 4/12x = 12x − 9x² − 4/12x = −(9x² − 12x + 4)/12x = −(3x − 2)²/12x
2) 1/3x − 1/2 = 1 ⋅ 2/3x ⋅ 2 − 1 ⋅ 3x/2 ⋅ 3x = 2 − 3x/6x
3) −(3x − 2)²/12x : 2 − 3x/6x = −(3x − 2)(3x − 2)/12x ⋅ 6x/2 − 3x = (2 − 3x)(3x − 2)/12x ⋅ 6x/2 − 3x = (2 − 3x)(3x − 2) ⋅ 6x/12x ⋅ (2 − 3x) = (2 − 3x)(3x − 2) ⋅ 6x : 6x(2 − 3x)/12x ⋅ (2 − 3x) : 6x(2 − 3x) = 3x − 2/2
4) 3x − 2/2 + 1 = 3x − 2/2 + 2/2 = 3x − 2 + 2/2 = 3x/2
в) 1 − (2/a − 2 − 2/a + 2) ⋅ (a − 3a + 2/4)
1) 2/a − 2 − 2/a + 2 = 2 ⋅ (a + 2)/(a − 2) ⋅ (a + 2) − 2 ⋅ (a − 2)/(a + 2) ⋅ (a − 2) = 2 ⋅ (a + 2) − 2 ⋅ (a − 2)/(a − 2) ⋅ (a + 2) = 2a + 4 − 2a + 4/(a − 2)(a + 2) = 8/(a − 2)(a + 2)
2) a − 3a + 2/4 = a/1 − 3a + 2/4 = a ⋅ 4/1 ⋅ 4 − 3a + 2/4 = 4a − 3a − 2/4 = a − 2/4
3) 8/(a − 2)(a + 2) ⋅ a − 2/4 = 8 ⋅ (a − 2)/(a − 2)(a + 2) ⋅ 4 = 8 ⋅ (a − 2) : 4(a − 2)/(a − 2)(a + 2) ⋅ 4 : 4(a − 2) = 2/a + 2
4) 1 − 2/a + 2 = a + 2/a + 2 − 2/a + 2 = a + 2 − 2/a + 2 = a/a + 2
г) (y² − 4) ⋅ (3/y + 2 − 2/y − 2) + 5
1) 3/y + 2 − 2/y − 2 = 3 ⋅ (y − 2)/(y + 2) ⋅ (y − 2) − 2 ⋅ (y + 2)/(y − 2) ⋅ (y + 2) = 3 ⋅ (y − 2) − 2 ⋅ (y + 2)/(y + 2)(y − 2) = 3y − 6 − 2y − 4/(y + 2)(y − 2) = y − 10/(y + 2)(y − 2)
2) (y² − 4) ⋅ y − 10/(y + 2)(y − 2) = (y² − 4)/1 ⋅ y − 10/(y + 2)(y − 2) = (y² − 4) ⋅ (y − 10)/1 ⋅ (y + 2)(y − 2) = (y² − 4) ⋅ (y − 10) : (y − 2)(y + 2)/1 ⋅ (y + 2)(y − 2) : (y − 2)(y + 2) = y − 10/1 = y − 10
3) y − 10 + 5 = y − 5