Question

3(x-1) 2(x+3) ------- + =2 3x-2 3x+2

Answer 1

Ответ:

3х-3*2х+6

3х*2х=3-6

6х=-3

Х=6:(-3)

Х=-2

-2=2

Объяснение:

Вроде так

Answer 2

To solve the equation:

3(x-1) 2(x+3) ------- + ------- = 2 3x-2 3x+2

First, let's simplify the expression by multiplying through by the denominators to eliminate the fractions:

[(3(x-1))/(3x-2)] + [(2(x+3))/(3x+2)] = 2

Now, let's clear the denominators by multiplying the entire equation by the common denominator, (3x-2)(3x+2):

[(3(x-1))(3x+2)] + [(2(x+3))(3x-2)] = 2(3x-2)(3x+2)

Simplifying further:

(3(x-1))(3x+2) + (2(x+3))(3x-2) = 2(9x^2-4)

Expand the terms:

(9x^2 - 3x - 2) + (6x^2 + 12x - 4) = 18x^2 - 8

Combine like terms:

9x^2 + 6x^2 - 3x + 12x + 2 - 4 = 18x^2 - 8

15x^2 + 9x - 2 = 18x^2 - 8

Move all terms to one side to form a quadratic equation:

0 = 18x^2 - 15x^2 - 9x + 8 - 2

0 = 3x^2 - 9x + 6

Now, let's solve this quadratic equation. We can either factor it or use the quadratic formula. In this case, factoring seems a bit complicated, so let's use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, a = 3, b = -9, and c = 6. Plugging in these values:

x = (-(-9) ± √((-9)^2 - 4(3)(6))) / (2(3))

x = (9 ± √(81 - 72)) / 6

x = (9 ± √9) / 6

x = (9 ± 3) / 6

Now, we have two possible solutions:

x₁ = (9 + 3) / 6 = 12 / 6 = 2

x₂ = (9 - 3) / 6 = 6 / 6 = 1

Therefore, the equation has two solutions: x = 2 and x = 1.