Question

9x-7/3x-2 - 4x-5/2x-3=1​

Answer 1

Ответ: x = 36

Пошаговое решение:

$9x-\frac{7}{3}x-2-4x-\frac{5}{2}x-3=1$

$-\frac{7}{3}x-\frac{5}{2}x+9x-4x-2-3=1$

$9x-\frac{7}{3}x-\frac{5}{2}x-4x-5=1$

$9x-\frac{7}{3}x-\frac{5}{2}x-4x=6$

$x=36$

Answer 2

To solve the equation:

$\frac{9x-7}{3x-2} - \frac{4x-5}{2x-3} = 1$

Let's start by finding a common denominator for the fractions. The common denominator is $(3x-2)(2x-3)$. Multiplying each term by the common denominator, we get:

$(2x-3)(9x-7) - (3x-2)(4x-5) = (3x-2)(2x-3)$

Expanding the expressions, we have:

$18x^2 - 27x - 14x + 21 - 12x^2 + 15x - 8x + 10 = 6x^2 - 9x - 4x + 6$

Combining like terms, we get:

$18x^2 - 27x - 14x + 21 - 12x^2 + 15x - 8x + 10 = 6x^2 - 9x - 4x + 6$

$6x^2 - 16x + 31 = 6x^2 - 13x + 6$

Subtracting $6x^2$ from both sides, we have:

$-16x + 31 = -13x + 6$

Subtracting $-13x$ from both sides, we have:

$-16x + 13x + 31 = 6$

Combining like terms, we get:

$-3x + 31 = 6$

Subtracting 31 from both sides, we have:

$-3x = -25$

Dividing both sides by -3, we get:

$x = \frac{-25}{-3}$

Simplifying the fraction, we have:

$x = \frac{25}{3}$

Therefore, the solution to the equation is $x = \frac{25}{3}$.