Canceling Negative Voltage in a Microphone Amplifier Circuit
+-3V is low for operational amplifier (op-amp), possible that some classical op-amp will not work!
For example, make a search in linear website (http://www.linear.com/products/Operational_Amplifiers_(Op_Amps)). Some of them can be supply between 3V and 6...12V. For example, LTC2050 could fit (redo the search, I have do that very quickly).
You can also download LTspice (http://www.linear.com/designtools/software/) and make some simulation to check that your schematics will work.
Then the signal is audio? You can also add serial capacitor after the op-amp to have a protection against accidental DC-voltage (start-up, shutdown, etc...).
Last advice: be careful with high-speed opamp! They can easily oscillate if there is no ground plan or too far decoupling cap.