Given equation:
The given equation is:

(sqrt(2 - x) / sqrt(2 + x)) = 3

Step 1: Cross-multiply
To solve the equation, we need to eliminate the square roots. We can start by cross-multiplying both sides of the equation:

sqrt(2 - x) * (sqrt(2 - x) + sqrt(2 + x)) = 3 * (sqrt(2 + x))

Step 2: Simplify the equation
Let's simplify the equation by expanding the expressions:

(2 - x) + sqrt((2 - x)(2 + x)) = 3 * sqrt(2 + x)

Simplifying the square root expression:

(2 - x) + sqrt(4 - x^2) = 3 * sqrt(2 + x)

Step 3: Isolate the square root terms
To solve for x, we need to isolate the square root terms on one side of the equation. Let's move all the terms containing square roots to one side:

sqrt(4 - x^2) = 3 * sqrt(2 + x) - (2 - x)

Expanding the right side:

sqrt(4 - x^2) = 3 * sqrt(2 + x) - 2 + x

Step 4: Square both sides
To eliminate the square root, we square both sides of the equation:

(4 - x^2) = (3 * sqrt(2 + x) - 2 + x)^2

Expanding the right side:

4 - x^2 = 9 * (2 + x) - 12 * sqrt(2 + x) + 4x - 4 * sqrt(2 + x) + 4 - 4x + x^2

Combining like terms:

4 - x^2 = 18 + 9x - 12 * sqrt(2 + x) - 4 * sqrt(2 + x) - 4x + x^2

Step 5: Simplify the equation
Let's simplify the equation by combining like terms:

-2x^2 - 13x + 14 = -16 * sqrt(2 + x)

Step 6: Isolate the square root
To solve for x, let's isolate the square root term:

16 * sqrt(2 + x) = 2x^2 + 13x - 14

Squaring both sides of the equation:

256 * (2 + x) = (2x^2 + 13x - 14)^2

Expanding the right side:

512 + 256x + 256x^2 = 4x^4 + 169x^2 + 196 - 52x^3 - 56x^2 + 364x

Step 7: Simplify the equation
Let's simplify the equation by combining like terms and rearranging:

4x^4 + 52x^3 - 169x^2 + 364x + 316 = 0

Step 8: Solve the equation
To solve the quartic equation, we can use numerical methods or factoring. Unfortunately, the equation does not factor easily