Question

А) (3х-2/х-4)=(3-5х/х-4)

Answer 1

(3x-2)/(x-4)=(3-5x)/(x-4), x≠4
3x-2=3-5x
3x+5x=3+2
8x=5
x=5/8, x≠4

Answer 2

$\frac{3x-2}{x-4} = \frac{3-5x}{x-4}$
$\left \{ {{3x-2 = 3-5x} \atop {x \neq 4}} \right.$
$\left \{ {{8x = 5} \atop {x \neq 4}} \right.$
$\left \{ {{x = \frac{5}{8} } \atop {x \neq 4}} \right.$
Ответ: $x = \frac{5}{8}$

Answer 3

To solve the equation:

(3x - 2)/(x - 4) = (3 - 5x)/(x - 4)

We can start by cross-multiplying:

(3x - 2)(x - 4) = (3 - 5x)(x - 4)

Expanding both sides of the equation:

3x^2 - 12x - 2x + 8 = 3x - 12 - 5x^2 + 20x

Combining like terms:

3x^2 - 14x + 8 = -5x^2 + 23x - 12

Moving all terms to one side of the equation:

3x^2 + 5x^2 - 14x - 23x + 8 + 12 = 0

8x^2 - 37x + 20 = 0

Now we can solve this quadratic equation by factoring or using the quadratic formula. Let's use the quadratic formula:

x = (-b ± √(b^2 - 4ac))/(2a)

For the equation 8x^2 - 37x + 20 = 0, the values of a, b, and c are:

a = 8 b = -37 c = 20

Substituting these values into the quadratic formula:

x = (-(-37) ± √((-37)^2 - 4 * 8 * 20))/(2 * 8)

Simplifying:

x = (37 ± √(1369 - 640))/16

x = (37 ± √729)/16

x = (37 ± 27)/16

Now we have two possible solutions:

x1 = (37 + 27)/16 = 64/16 = 4

x2 = (37 - 27)/16 = 10/16 = 5/8

Therefore, the solutions to the equation are x = 4 and x = 5/8.