Question

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.

Answer 1

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.