Question

Розв'яжіть рівняння.
$\frac{x {}^{2} - 16}{x + 2} = 0$
$\frac{x - 2}{x + 3} = \frac{x - 4}{x + 5}$
$\frac{2x - 1}{2x + 1} + \frac{2x}{2x - 1} = 2$
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Answer 1

Ответ:

1) x = ±4

2) x = -0.5

3) x = 1,5

Объяснение:

1)

$x^2 - 16 = 0 | *(x+2)\\x^2 = 16\\x = \pm 4$

2)

$(x-2)(x+5) = (x-4)(x+3) | *(x+3)(x+5)\\x^2 + 3x - 10 = x^2 - x - 12\\3x - 10 = -x - 12\\4x - 10 = -12\\4x = -2\\x = -0.5$

3)

$(2x-1)(2x-1) + 2x(2x+1) = 2(2x+1)(2x-1) | * (2x-1)(2x+1) \\4x^2 - 4x + 1 + 4x^2 + 2x = 8x^2 - 2\\8x^2 - 2x + 1 = 8x^2 - 2\\-2x+1 = - 2\\-2x = -3\\2x = 3\\x = 3/2\\x = 1,5$

Answer 2

Объяснение:

(х² - 16)/(х + 2) = 0 ОДЗ: х ≠ -2

х² - 16 = 0

х² = 16

х = ± 4

(х - 2)/(х + 3) = (х - 4)/(х + 5) ОДЗ: х ≠ -3; х ≠ -5

(х - 2)*(х + 5) = (х + 3)*(х - 4)

х² + 5х - 2х - 10 = х² - 4х + 3х - 12

х² + 3х - 10 = х² - х - 12

3х - 10 = -х - 12

3х + х = -12 + 10

4х = -2

х = -2 : 4

х = -0,5

(2х - 1)/(2х + 1) + 2х/(2х - 1) = 2 ОДЗ: х ≠ -1/2; х ≠ 1/2

( (2х-1)² + 2х(2х+1) )/( (2х+1)(2х-1) ) = 2

(4х² - 4х + 1 + 4х² + 2х)/ (2х+1)(2х-1) ) = 2

(8х² - 2х + 1)/( (2х+1)(2х-1) ) = 2

8х² - 2х + 1 = 2(2х + 1)(2х - 1)

8х² - 2х + 1 = 2(4х² - 1)

8х² - 2х + 1 = 8х² - 2

-2х + 1 = -2

-2х = -2 - 1

-2х = -3

х = -3 : (-2)

х = 1,5