The expression $\frac{x-3}{4x}$ is equal to zero for what value of $x$?
The fraction is equal to zero if the numerator is equal to zero. Thus, $x-3=0$, so $x=\boxed{3}$. (Note that at this $x$ value, the denominator is not equal to zero.)
3
Level 1
Algebra
Problem: The expression $\frac{x-3}{4x}$ is equal to zero for what value of $x$?
Solution:<|START_OF_LATENT|><|PRIOR_PREFIX|>To determine when the expression $\frac{x-3}{4x}$ equals zero, we need to analyze the fraction. A fraction is equal to zero when its numerator is zero, provided the denominator is not zero. 

The numerator of the expression is $x - 3$. Setting this equal to zero gives the equation:

1. $x - 3 = 0$

Solving for $x$ involves adding 3 to both sides:

2. $x = 3$

Next, we must ensure that this value does not make the denominator zero. The denominator is $4x$. Substituting $x = 3$ into the denominator:

3. $4(3) = 12$, which is not zero.

Since the denominator is not zero when $x = 3$, this value is valid. Therefore, the expression $\frac{x-3}{4x}$ is equal to zero when $x$ is $3$. 

The final answer is $3$.<|END_OF_LATENT|> The final answer is $3$.