Final answer:
The value that makes the denominator zero in the equation (3x)/(x+3)=8-(9)/(x+3) is x = -3. This value is not part of the domain of the function and must be discarded when solving the equation.
Step-by-step explanation:
The student has asked about finding the value or values of the variable that makes the denominator zero in the equation (3x)/(x+3)=8-(9)/(x+3). To find the value that makes the denominator zero, we set the denominator equal to zero and solve for the variable. Hence, x+3 = 0, which simplifies to x = -3. This is the value of the variable that would make the denominator zero. It is important to note that when you have a denominator in an equation, dividing by zero is undefined; therefore, the solution cannot include this value of x in its domain.
However, the fact that x = -3 makes the denominator zero does not constitute it as a solution to the equation; instead, it represents a value that is not part of the domain of the function. If we were to solve for x in this equation properly, we would clear the denominators by multiplying both sides of the equation by (x+3), which ensures we do not divide by zero, thus maintaining the equality. In the process of solving, any result that gives x = -3 must be discarded.