To solve the equation 1/(a*b*x) = 1/(a*1/b*1/x) for x, we can follow these steps:

Step 1: Simplify the equation
To simplify the equation, we need to simplify the fractions on both sides. Let's start by simplifying the right side of the equation.

1/(a*1/b*1/x) can be rewritten as 1/(a/b*x) since dividing by a fraction is the same as multiplying by its reciprocal.

So, the equation becomes:
1/(a*b*x) = 1/(a/b*x)

Step 2: Apply the reciprocal property
To make the equation easier to work with, we can apply the reciprocal property by swapping the numerator and denominator on the right side of the equation.

The equation now becomes:
1/(a*b*x) = b/a*x

Step 3: Cross-multiply
To eliminate the denominators, we can cross-multiply both sides of the equation.

(a*b*x)(b/a*x) = (1)(1)

Simplifying the left side:
(a*b*x)(b/a*x) = (abx)(bx/a)

Step 4: Simplify the equation
Simplifying the equation further, we get:
(abx)(bx/a) = 1

Expanding the brackets:
(abx)(bx/a) = abx^2/a

Step 5: Cancel out common factors
On the left side of the equation, we have (abx)(bx/a). The a in the numerator cancels out with the a in the denominator, leaving us with:
(abx)(bx/a) = bx^2

Step 6: Solve for x
Now, we can solve for x by dividing both sides of the equation by bx^2.

(abx)(bx/a) / (bx^2) = bx^2 / (bx^2)

Simplifying the left side:
(abx)(bx/a) / (bx^2) = b/a

Simplifying the right side:
bx^2 / (bx^2) = 1

So, we have:
b/a = 1

Step 7: Solve for x
Since b/a = 1, we can substitute it back into the equation:

1/(a*b*x) = b/a*x

1/(a*b*x) = 1*x

1/(a*b*x) = x

Multiplying both sides of the equation by a*b*x, we get:
1 = x(a*b*x)

Simplifying further:
1 = abx^2

Finally, dividing both sides by ab, we find:
x^2 = 1/ab

Taking the square root of both sides, we obtain:
x = ±√(1/ab)

Therefore, the solutions for x are x = √(1/ab) and x = -√(1/ab).

Note: The above steps outline the process to solve the given equation. However, it's important to double-check the solution and consider any potential restrictions on the variables a and b to ensure the validity of the obtained results.