Question

(x^2-x-6)/x-8x/(x^2-x-6)=2

Answer 1

Ответ:

Объяснение:/ едто умножить?

Answer 2

To solve the given equation, we'll first simplify the equation and then solve for the value of "x". Let's break down the steps:

Given equation:

$\frac{x^2-x-6}{x} - \frac{8x}{x^2-x-6} = 2$

Step 1: Factor the denominators of the fractions on the left side.

The denominator $x$ can be factored as $x(x-1)$, and the denominator $x^2-x-6$ can be factored as $(x-3)(x+2)$.

So, the equation becomes:

$\frac{x^2-x-6}{x(x-3)(x+2)} - \frac{8x}{x(x-3)(x+2)} = 2$

Step 2: Combine the fractions over a common denominator.

$\frac{x^2-x-6-8x}{x(x-3)(x+2)} = 2$

Simplify the numerator:

$\frac{x^2 - 9x - 6}{x(x-3)(x+2)} = 2$

Step 3: Multiply both sides by the denominator to eliminate the fraction.

$x^2 - 9x - 6 = 2x(x-3)(x+2)$

Step 4: Distribute and simplify the right side.

$x^2 - 9x - 6 = 2x(x^2 - x - 6)$

$x^2 - 9x - 6 = 2x^3 - 2x^2 - 12x$

Step 5: Rearrange the equation to form a cubic equation on one side.

$2x^3 - x^2 - 3x - 6 = 0$

Now, we have a cubic equation $2x^3 - x^2 - 3x - 6 = 0$. Solving cubic equations generally involves finding the roots using numerical methods or specialized techniques like the Rational Root Theorem, the cubic formula, or software tools.

Unfortunately, cubic equations don't always have straightforward analytical solutions like quadratic equations. You might need to use numerical methods or software to approximate the solutions.