For what values of x is x/[x(3x-4)] undefined?
To determine the values of x for which the expression is undefined, we need to identify any potential values of x that would make the denominator equal to zero. Recall that division by zero is undefined.
In this case, the given expression is x/[x(3x-4)]. The denominator is x(3x-4). Therefore, we need to find the values of x that would make the denominator equal to zero.
Setting the denominator equal to zero and solving for x, we have:
x(3x-4) = 0
To solve this equation, we set each factor equal to zero:
x = 0 (from the first factor)
3x - 4 = 0 (from the second factor)
For the first factor, x can be 0.
For the second factor, we solve the equation:
3x - 4 = 0
3x = 4
x = 4/3
Therefore, x can be either 0 or 4/3.
However, note that in the original expression, the numerator is also x. So when x is 0, the entire expression becomes 0/0, which leads to an indeterminate form.
Therefore, the values of x for which the expression is undefined are x = 0 and x = 4/3, excluding x = 0 as it results in an undefined expression.