If you consider the case when one of the input signals is silent its voltage will be zero. This will be exactly the same as connecting that input to ground. The result: no change in amplification of the other signals.
The output of your opamp will be given by the formula
Vout=(1 + R2/R1) (Signal1 + Signal2 + Signal3) / 3
What this is telling us is that the three signals are summed and divided by three. (Consider the case where two of the signals are silent and at zero volts. The one remaining signal is fed in via a 24 kΩ resistor with two others pulling it down by 12 kΩ resulting in 1/3 the signal level at the non-inverting input.)
To compensate for the division by three, the gain of the amplifier has been set to three also by
1 + R2 / R1 = 1 + 24 / 12 = 1 + 2 = 3