Question

3x-5/x-1 -2x-5/x-2=1

Answer 1

Ответ: х=3

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

ОДЗ: х-1≠0 х≠1

х-2≠0 х≠2

$\frac{(x - 2) \times (3x - 5) - (x - 1) \times (2x - 5)}{(x - 1) \times (x - 2)} = 1$

$\frac{3 {x}^{2} - 5x - 6x + 10 - (2 {x}^{2} - 5x - 2x + 5) }{(x - 1)(x - 2)} = 1$

$\frac{3 {x}^{2} - 5x - 6x + 10 - 2 {x}^{2} + 7x - 5 }{(x - 1)(x - 2)}$

$\frac{ {x}^{2} - 4x + 5 }{(x - 1)(x - 2)}$

${x}^{2} - 4x + 5 = (x - 1)(x - 2)$

${x}^{2} - 4x + 5 = {x}^{2} - 2x - x + 2$

$- 4x + 5 = - 2x - x + 2$

$- 4x + 5 = - 3x + 2$

$- 4x + 3x = 2 - 5$

$- x = - 3$

$x = 3$

Answer 2

To solve the equation (3x - 5) / (x - 1) - (2x - 5) / (x - 2) = 1, you'll need to find the value(s) of x that satisfy the equation. To do this, let's start by finding a common denominator for the fractions on the left side of the equation:

The common denominator is (x - 1)(x - 2), so we can rewrite the equation as follows:

[(3x - 5)(x - 2) - (2x - 5)(x - 1)] / [(x - 1)(x - 2)] = 1

Now, let's simplify the equation:

Expand the terms in the numerator:

[3x^2 - 6x - 5x + 10 - (2x^2 - 2x - 5x + 5)] / [(x - 1)(x - 2)] = 1

Combine like terms:

[3x^2 - 6x - 5x + 10 - 2x^2 + 2x + 5x - 5] / [(x - 1)(x - 2)] = 1

Simplify further:

(x^2 - 4x + 5) / [(x - 1)(x - 2)] = 1

Now, cross-multiply:

x^2 - 4x + 5 = (x - 1)(x - 2)

Expand the right side:

x^2 - 4x + 5 = x^2 - 3x + 2

Now, bring all terms to one side of the equation:

x^2 - 4x + 5 - x^2 + 3x - 2 = 0

Simplify:

-x + 3 = 0

Now, isolate x:

x = 3

So, the solution to the equation is x = 3. You can check this solution by plugging it back into the original equation and see if it holds true.