Solve 4 over x minus 4 equals the quantity of x over x minus 4, minus four thirds for x and determine if the solution is extraneous or not.

We mathematically express the given such that it becomes,

4 / (x - 4) = x / (x - 4) - 4/3

To answer this, multiply the equation by 3 (x - 4) since this is the least common multiple (LCM).

4 (3) = (3) (x) - 4 (x - 4)

Simplifying,

12 = 3x - 4x + 16

4 = - 4x

The value of x should be equal to - 1.

The calculated value of y can be calculated.