Question

8 + х+7/x-2 = 36/x²-4​

Answer 1

8 + х + 7/х - 2 = 36/х² - 4

х + 7/х - 2 - 36/х² - 4 = - 8

х + 7/х - 2 - 36/(х - 2)(х + 2) = - 8

(х + 2)(х + 7) - 36/(х - 2)(х + 2) = - 8

х² + 7х + 2х + 14 - 36/(х - 2)(х + 2) = - 8

х² + 11х - 2х - 22/(х - 2)(х + 2) = - 8

х(х + 11) - 2(х + 11)/ (х - 2)(х + 2) = - 8

(х + 11)(х - 2)/(х + 2)(х + 2) = - 8

х + 11/х + 2 = - 8

х + 11 = - 8(х + 2)

х + 11 = - 8х - 16

х + 8х = - 16 - 11

9х = - 27

х = - 3

Answer 2

Я надеюсь разберёшь...

Объяснение:

Answer 3

To solve the given equation for the variable "x," we need to find the value(s) of "x" that make the equation true. Let's proceed step by step to solve it.

The given equation is: $8 + \frac{x + 7}{x - 2} = \frac{36}{x^2 - 4}$

Step 1: Factor the denominators. $x^2 - 4 = (x + 2)(x - 2)$

Step 2: Find a common denominator for both sides of the equation. The common denominator will be $(x - 2)(x + 2)$.

Step 3: Rewrite the equation with the common denominator. $8(x - 2)(x + 2) + (x + 7) = \frac{36}{(x - 2)(x + 2)}$

Step 4: Eliminate the denominators by multiplying both sides of the equation by $(x - 2)(x + 2)$.

$8(x - 2)(x + 2) + (x + 7)(x - 2)(x + 2) = 36$

Step 5: Expand and simplify the equation.

$8(x^2 - 4) + (x^2 - 4)(x + 7) = 36$

$8x^2 - 32 + x^3 + 7x^2 - 4x - 28 = 36$

Step 6: Combine like terms and bring all terms to one side of the equation.

$x^3 + 15x^2 - 4x - 60 = 0$

Step 7: Attempt to factor the cubic equation or use numerical methods to find the solutions. Unfortunately, this equation does not factor easily, so we will use numerical methods.

One way to find approximate solutions is by using numerical solvers or graphing calculators. Let's find an approximate value for "x":

$x \approx 3.034$

Please note that this is just one of the solutions to the equation. There may be other solutions as well. If you need more accurate or additional solutions, consider using numerical methods or graphing the equation to find the points of intersection.