Voicemail (or an answering machine) and fax machine can be on the same phone line. However, only one of the two can answer the phone when it rings.
If both voicemail and a fax machine are configured to respond to the phone, whichever is set to pick up after the fewer number of rings will answer the call when the phone rings.
There is no way for the voicemail or the fax system to “check” if the call is a fax or not.
Alternative #1 – two different phone lines
With two phone lines, the fax number and the voicemail both have their own phone line. When one is in operation, the other is still completely available.
The challenge with this approach is cost. Most phone providers will charge close to the same for the second phone line as they do for the first. Installing the second phone line will have a cost as well as wires will need to be run or connected in the house.
Alternative #2 – one phone line with two different phone numbers and a distinctive ring
Some phone providers offer two phone numbers on the same line, and each has a different ring.
Some fax machines have technology call DRPD (distinctive ring pattern detection) that can tell if the phone is ringing for the regular phone line or the fax number.
While some providers offer the second phone number, not all of them have a way to show the other number’s caller id when calling out.
Alternative #3 – an online fax service
An online fax service is a fax service hosted by a company that takes care of phone lines, software, and everything involved with fax. Faxes are sent and received through their software, web interface, smartphone, or by email.
Most fax services cost less on a monthly basis than an entire extra phone line, but more than adding a second phone number to a phone line.