To solve the equation \(\frac{x+3}{4} = \frac{x-1}{3}\), we can cross-multiply:
\[ 3(x + 3) = 4(x - 1) \]
Now, distribute both sides:
\[ 3x + 9 = 4x - 4 \]
Next, we can isolate \(x\) by moving all terms involving \(x\) to one side and constant terms to the other:
\[ 9 + 4 = 4x - 3x \]
This simplifies to:
\[ 13 = x \]
Thus, the solution is:
\[ \boxed{13} \]