To solve the equation, let's first simplify both sides:

Starting with the left side:
-2/4x - 4 - 1/x - 1

To combine the fractions, we need a common denominator. The common denominator for 4x and x is 4x. So, let's rewrite the equation:

(-2 - 4x)/4x - 1/x - 1

Now, let's find a common denominator for 4x and x:

(-2 - 4x)/4x - x/x - 1

(-2 - 4x - x)/4x - 1

(-2 - 5x)/4x - 1

Now, let's simplify the right side of the equation:

x/(1-x)(x+1)

To simplify further, let's factor the denominator:

x/[(1-x)(x+1)]

Now, let's combine the fractions on the right side:

(-2 - 5x)/4x - 1 = x/[(1-x)(x+1)]

To eliminate the denominators, let's multiply both sides of the equation by (4x)(1-x)(x+1):

[(4x)(1-x)(x+1)][(-2 - 5x)/4x - 1] = [(4x)(1-x)(x+1)][x/[(1-x)(x+1)]]

Simplifying the equation:

(-2 - 5x)(1-x)(x+1) - (4x)(1-x)(x+1) = x

Expanding the equation:

(-2 - 5x)(x^2 - x + x - 1) - (4x)(x^2 - x + x - 1) = x

(-2 - 5x)(x^2 - 1) - (4x)(x^2 - 1) = x

Now, let's distribute and simplify:

(-2 - 5x)(x^2) - (-2 - 5x)(1) - (4x)(x^2) + (4x)(1) = x

-2x^2 - 5x^3 - (-2 - 5x) - 4x^3 + 4x - x = 0

-2x^2 - 5x^3 + 2 + 5x - 4x^3 + 4x - x = 0

-2x^2 - 5x^3 - 4x^3 - x + 5x + 4x + 2 = 0

-2x^2 - 9x^3 + 8x + 2 = 0

At this point, it seems that the equation cannot be simplified further.