Question

2x-9/2x-5-3x/2-3x=2 Решите уравнение с проверкой.

Answer 1

/ этот знак деления или дроби?

Answer 2

To solve the equation $2x - \frac{9}{2x - 5} - \frac{3x}{2} - 3x = 2$, follow these steps:

Step 1: Simplify the fractions: Let's start by simplifying the fractions in the equation.

$\frac{9}{2x - 5}$ can be rewritten as $\frac{9}{2x} - \frac{9}{5}$ using the difference of squares rule.

So the equation becomes: $2x - \frac{9}{2x} + \frac{9}{5} - \frac{3x}{2} - 3x = 2$

Step 2: Get rid of denominators: To eliminate the fractions, we can multiply the entire equation by the least common multiple (LCM) of the denominators, which is 10x.

$10x \cdot 2x - 10x \cdot \frac{9}{2x} + 10x \cdot \frac{9}{5} - 10x \cdot \frac{3x}{2} - 10x \cdot 3x = 10x \cdot 2$

Simplifying further: $20x^2 - 45 + 18x - 15x^2 - 30x = 20x$

Step 3: Combine like terms: Combine the like terms on the left side of the equation:

$20x^2 - 15x^2 + 18x - 30x - 45 = 20x$

$5x^2 - 12x - 45 = 20x$

Step 4: Move all terms to one side of the equation: Move all terms to one side of the equation to set it to zero:

$5x^2 - 12x - 20x - 45 - 20x = 0$

$5x^2 - 32x - 45 = 0$

Step 5: Solve the quadratic equation: Use the quadratic formula to find the values of x:

The quadratic formula is $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$.

For our equation, a = 5, b = -32, and c = -45.

$x = \frac{-(-32) \pm \sqrt{(-32)^2 - 4 \cdot 5 \cdot (-45)}}{2 \cdot 5}$

$x = \frac{32 \pm \sqrt{1024 + 900}}{10}$

$x = \frac{32 \pm \sqrt{1924}}{10}$

$x = \frac{32 \pm \sqrt{4 \cdot 481}}{10}$

$x = \frac{32 \pm 2\sqrt{481}}{10}$

Step 6: Find the solutions: Now, we have two potential solutions for x:

$x_1 = \frac{32 + 2\sqrt{481}}{10}$

$x_2 = \frac{32 - 2\sqrt{481}}{10}$

Step 7: Check the solutions: Let's verify if these solutions are correct by substituting them back into the original equation:

For $x_1 = \frac{32 + 2\sqrt{481}}{10}$:

$2\cdot \frac{}{}$ 0 0