Алгебра 8 класс учебник Мерзляк, Полонский ответы – номер 211

1) 5/x² – 4 + 2x/x + 2 = 2
5 + 2x(x – 2)/(x – 2)(x + 2) – 2 = 0
5 + 2x² – 4x – 2(x² – 4)/(x – 2)(x + 2) – 2 = 0
5 + 2x² – 4x – 2x² + 8/(x – 2)(x + 2) – 2 = 0
– 4x + 13/(x – 2)(x + 2) – 2 = 0
(x – 2)(x + 2) ≠ 0
x ≠ 2 или x ≠ – 2
– 4x + 13 = 0
– 4x = – 13
x = 13/4
x = 31/4
Ответ: x = 31/4.
2) 2/6x + 1 + 3/6x – 1 = 30x + 9/36x² – 1
2/6x + 1 + 3/6x – 1 – 30x + 9/(6х – 1)(6х + 1) = 0
2(6x – 1) + 3(6x + 1) – 30x – 9/(6х – 1)(6х + 1) = 0
12x – 2 + 18x + 3 – 30x – 9/(6х – 1)(6х + 1) = 0
– 8/(6х – 1)(6х + 1) = 0
– 8 = 0
Ответ: корней нет.
3) 6x + 14/x² – 9 + 7/x² + 3x = 6/x – 3
6x + 14/x² – 9 + 7/x² + 3x – 6/x – 3 = 0
x(6x + 14) + 7(x – 3) – 6x(x + 3)/x(x – 3)(x + 3) = 0
6x² + 14x + 7x – 21 – 6x² – 18x/x(x – 3)(x + 3) = 0
3x – 21/x(x – 3)(x + 3) = 0
x(x – 3)(x + 3) ≠ 0
x ≠ 0 или x – 3 ≠ 0 или х + 3 ≠ 0
              х ≠ 3               х ≠ – 3
3x – 21 = 0
3x = 21
x = 7
Ответ: 7.
4) 2y² + 5/1 – y² + y + 1/y – 1 = 4/y + 1
2y² + 5/1 – y² + y + 1/y – 1 – 4/y + 1 = 0
2y² + 5 – (y + 1)(y + 1) – 4(1 – y)/(1 – y)(1 + y) = 0
2y² + 5 – y² – 2y – 1 – 4 + 4y/(1 – y)(1 + y) = 0
y² + 2y/(1 – y)(1 + y) = 0
y(y + 2)/(1 – y)(1 + y) = 0
(1 – y)(1 + y) ≠ 0
1 – y ≠ 0 или 1 + y ≠ 0
y ≠ 1                y ≠ – 1
y(y + 2) = 0
y = 0 или y + 2 = 0
              y = – 2
Ответ: 0; – 2.
5) 2x – 1/2x + 1 = 2x + 1/2x – 1 + 4/1 – 4x²
2x – 1/2x + 1 – 2x + 1/2x – 1 – 4/1 – 4x² = 0
2x – 1/2x + 1 – 2x + 1/2x – 1 + 4/(2x – 1)(2x + 1) = 0
(2x – 1)(2x – 1) – (2x + 1)(2x + 1) + 4/(2x – 1)(2x + 1) = 0
4x² – 4x + 1 – 4x² – 4x – 1 + 4/(2x – 1)(2x + 1) = 0
– 8x + 4/(2x – 1)(2x + 1) = 0
(2x – 1)(2x + 1) ≠ 0
2x – 1 ≠ 0 или 2x + 1 ≠ 0
2х ≠ 1      2х ≠ – 1
х ≠ 0,5      х ≠ – 0,5
– 8x + 4 = 0
– 8x = – 4
х = 0,5
Ответ: корней нет.
6) 7/(x + 2)(x – 3) – 4/(x – 3)² = 3/(x + 2)²
7/(x + 2)(x – 3) – 4/(x – 3)² – 3/(x + 2)² = 0
7(x + 2)(x – 3) – 4(x + 2)² – 3(x – 3)²/(x + 2)²(x – 3)² = 0
7x² – 7x – 42 – 4x² – 16x – 16 – 3x² + 18x – 27/(x + 2)²(x – 3)² = 0
– 5x – 85/(x + 2)²(x – 3)² = 0
(x + 2)²(x – 3)² ≠ 0
x + 2 ≠ 0 или x – 3 ≠ 0
x ≠ – 2              x ≠ 3
– 5x – 85 = 0
– 5x = 85
x = – 17
Ответ: – 17.
7) 2x – 1/x + 4 – 3x – 1/4 – x = 6x + 64/x² – 16 + 4
2x – 1/x + 4 – 3x – 1/4 – x – 6x + 64/x² – 16 – 4 = 0
(2x – 1)(x – 4) + (3x – 1)(x + 4) – 6x – 64 – 4(x² – 16)/(x + 4)(x – 4) = 0
2x² – 8x – x + 4 + 3x² + 12x – x – 4 – 6x – 64 – 4x² + 64/(x + 4)(x – 4) = 0
x² – 4x/(x + 4)(x – 4) = 0
(x + 4)(x – 4) ≠ 0
x + 4 ≠ 0 или x – 4 ≠ 0
x ≠ – 4              x ≠ 4
x² – 4x = 0
x(x – 4) = 0
x = 0 или x – 4 = 0
                 x = 4
Ответ: 0.
8) 2x – 6/x² – 36 – x – 3/x² – 6x – x – 1/x² + 6x = 0
2x – 6/(x – 6)(x + 6) – x – 3/x(x – 6) – x – 1/x(x + 6) = 0.
x(2x – 6) – (x – 3)(x + 6) – (x – 1)(x – 6)/x(x – 6)(x + 6) = 0
2x² – 6x – x² – 3x + 18 – x² + 7x – 6/x(x – 6)(x + 6) = 0
– 2x + 12/x(x – 6)(x + 6) = 0
x(x – 6)(x + 6) ≠ 0
x ≠ 0 или x – 6 ≠ 0 или x + 6 ≠ 0
                 x ≠ 6               x ≠ – 6
– 2x + 12 = 0
– 2x = – 12
x = 6
Ответ: корней нет.