To solve the equation x - 1/y - 4/xy = -1, we can start by simplifying the expression.

First, let's find a common denominator for the fractions. The common denominator for y and xy is xy.

So, x - 1/y - 4/xy can be written as (x * xy - 1 * xy - 4) / xy.

Simplifying further, we have (x^2y - xy - 4) / xy = -1.

Now, let's multiply both sides of the equation by xy to eliminate the denominator:

xy * (x^2y - xy - 4) / xy = -1 * xy.

This simplifies to x^2y - xy - 4 = -xy.

Next, let's combine like terms:

x^2y - xy + xy - 4 = 0.

The xy terms cancel out, leaving us with:

x^2y - 4 = 0.

Now, let's solve for x:

x^2y = 4.

Divide both sides by y:

x^2 = 4/y.

Take the square root of both sides:

x = ±√(4/y).

Therefore, the solution to the equation x - 1/y - 4/xy = -1 is x = ±√(4/y).