How do you add rational expressions?

You have to have a common denominator, just like with any other fractions. To get (a-1) into the first one you have to multiply the numerator and denominator by (a-1) to get (a-1)(4a)/(a-1)(a-2). To get (a-2) into the second one, multiply the numerator and denominator by (a-2) to get (a-2)(6)/(a-2)(a-1). Now you have, after FOILing out the numerator, (4a^2-4a) + (6a-12)/(a-1)(a-2). Simplifying the numerator gives you 4a^2+2a-12/(a-1)(a-2).