Question

(3х-1)/х -4/(х-2)= (10-9х)/(х²-2х) *

Answer 1

Ответ:

-1 целая 1\3

Пошаговое объяснение:

Пошаговое решение на прикрепленной фотографии.

Answer 2

To solve the given equation:

$\frac{3x-1}{x} - \frac{4}{x-2} = \frac{10-9x}{x^2-2x}$

First, let's simplify the equation by finding a common denominator:

$\frac{(3x-1)(x-2)}{x(x-2)} - \frac{4x}{x(x-2)} = \frac{10-9x}{x(x-2)}$

Now, combine the numerators over the common denominator:

$\frac{(3x-1)(x-2) - 4x}{x(x-2)} = \frac{10-9x}{x(x-2)}$

Expanding the numerator on the left side:

$\frac{3x^2 - 7x + 2 - 4x}{x(x-2)} = \frac{10-9x}{x(x-2)}$

Combining like terms:

$\frac{3x^2 - 11x + 2}{x(x-2)} = \frac{10-9x}{x(x-2)}$

Now, since both sides have the same denominator, we can equate the numerators:

$3x^2 - 11x + 2 = 10 - 9x$

Rearranging the terms:

$3x^2 - 11x + 9x + 2 - 10 = 0$

Simplifying:

$3x^2 - 2x - 8 = 0$

Now, we can attempt to factor the quadratic equation:

$3x^2 - 2x - 8 = (x-2)(3x+4) = 0$

Setting each factor equal to zero:

x - 2 = 0 or 3x + 4 = 0

Solving for x in each equation:

x = 2 or 3x = -4 => x = -4/3

Therefore, the solution to the given equation is x = 2 and x = -4/3.