@xiggi, I completely agree that that is the key on the SAT. You have to start by thinking about what you are going to do and why you are going to do it. It is a problem solving test more than it is a Math test IMO. I personally tell people not to write anything down when they first read a question because in my opinion that prevents people from thinking about the question before they “knee-jerk” into a particular approach.
I mean in above question they are giving you (4-x) / (2+x) = x and they are asking for x^2 + 3x - 4, so there must be some way to take the given information and solve for what they are asking for. And basically you can either manipulate that first equation and solve for x and then plug x into the quadratic or consider that since they are very suspiciously not asking for x but for the value of an expression (the quadratic) that maybe, just maybe, you could solve for that expression directly.
And here is another thing that I like. Even if you don’t know how to manipulate that first equation, you could just plug in values for x until you find one that works and then take that value of x and plug it into the quadratic. I have seen people who are not good at algebra do this and get the question right. Obviously you would be assuming that x will be a value that you can easily stumble upon, but usually on the SAT it is so it’s not bad idea to just plug in values like x = 1, 2, 3, 0, -1, -2, -3 and hope that you get something. If you know that you aren’t comfortable doing it algebraically then at least you have something. And of course x=1 works so you would quickly get that and then plug that value into the quadratic and have the right answer.
And @MITer94 I like that variety of the question a lot because a lot of people get the version that I posted correct simply because they get lucky and assume that the quadratic equals 0, but in your version that wouldn’t happen so people who didn’t really think carefully about what they were doing would probably not get the question right!