To determine the value of \( x \) that causes the rational equation \( \frac{3}{x+5} = \frac{1}{x+5} + 4 \) to be undefined, we need to identify the values of \( x \) for which the denominators become zero.
The denominators in the equation are \( x + 5 \). The equation will be undefined when:
\[ x + 5 = 0 \]
Solving for \( x \):
\[ x = -5 \]
Thus, the equation is undefined when \( x = -5 \).