5/х^2-4 +2х/х+2=2

To solve the equation, we first need to find a common denominator for the fractions on the left side of the equation.

The denominators are (x^2 - 4) and (x + 2). The common denominator is (x^2 - 4)(x + 2).

Next, we multiply each term by the common denominator to clear the fractions:

[(x^2 - 4)(x + 2)] * (5/(x^2 - 4)) + [(x^2 - 4)(x + 2)] * (2x/(x + 2)) = 2 * [(x^2 - 4)(x + 2)]

Simplifying the equation:

5(x + 2) + 2x(x^2 - 4) = 2((x^2 - 4)(x + 2))

Distribute the terms:

5x + 10 + 2x^3 - 8x + 8 = 2(x^3 - 4x + 2x^2 - 8)

Combine like terms:

2x^3 - 8x + 8x^2 + 2x^2 + 5x - 10 = 2x^3 - 8x + 4x^2 - 16

Simplify:

2x^3 + 10x^2 + 5x - 10 = 2x^3 + 4x^2 - 8x - 16

Now, we can cancel out the 2x^3 terms:

10x^2 + 5x - 10 = 4x^2 - 8x - 16

Combine like terms:

10x^2 - 4x^2 + 5x + 8x - 10 + 16 = 0

6x^2 + 13x + 6 = 0

Now, we can solve this quadratic equation:

(2x + 3)(3x + 2) = 0

Setting each factor equal to zero:

2x + 3 = 0 or 3x + 2 = 0

Solving for x:

2x = -3 or 3x = -2

x = -3/2 or x = -2/3

So, the solutions to the equation are x = -3/2 and x = -2/3.