problems such as this should be worked directly within Algebrator; once the software is installed (this message will includes links to free trial versions), press the Wizard button, expand the Functions tab and you will see a wizard specifically for finding the domain of a function, along with adding, subtracting, multiplying and dividing functions and much more

If you do not currently own Algebrator, then please use one of the following links to obtain a free trial of the program:

Windows: https://www.softmath.com/tr/alg51win-tr-en.exe

Mac: https://www.softmath.com/tr/alg51mac-tr-en.dmg