Question

(2х-5)/х - х/(2х-5) = 0

Answer 1

X1=5/3
X2=5
P.s /-дробная черта

Answer 2

To solve the equation $\frac{2x-5}{x} - \frac{x}{2x-5} = 0$, you can follow these steps:

1. Find a common denominator for the fractions on the left side. In this case, the common denominator is $x(2x-5)$.

2. Rewrite each fraction with the common denominator:

   $\frac{(2x-5)(2x-5)}{x(2x-5)} - \frac{x(x)}{x(2x-5)} = 0$

3. Now, combine the fractions:

   $\frac{(2x-5)(2x-5) - x^2}{x(2x-5)} = 0$

4. Expand and simplify the numerator:

   $(4x^2 - 20x + 25) - x^2 = 0$

5. Combine like terms:

   $3x^2 - 20x + 25 = 0$

6. This is now a quadratic equation. To solve it, you can use the quadratic formula:

   $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

   In this case, $a = 3$, $b = -20$, and $c = 25$. Plug these values into the formula:

   $x = \frac{-(-20) \pm \sqrt{(-20)^2 - 4(3)(25)}}{2(3)}$

   $x = \frac{20 \pm \sqrt{400 - 300}}{6}$

   $x = \frac{20 \pm \sqrt{100}}{6}$

7. Simplify the square root:

   $x = \frac{20 \pm 10}{6}$

Now, you have two possible solutions:

1. $x = \frac{20 + 10}{6} = \frac{30}{6} = 5$

2. $x = \frac{20 - 10}{6} = \frac{10}{6} = \frac{5}{3}$

So, the solutions to the equation are $x = 5$ and $x = \frac{5}{3}$.