Explanation for Question 12 From the Math (No Calc) Section on the 2019 October Sat
Not for question number 12. Um, 2 we're asked to solve for the value of X, 3 right? But if you want to solve for the value of X, 4 what we need to do is get all of our fractions to have a 5 common denominator. That way we can actually subtract these 6 two fractions here, like it wants us to, but the only way to do 7 that is to make sure that all of our fractions have the same denominator. 8 And in this case, the best common denominator is going to be X squared 9 minus nine. Because if we look at our other two denominators, 10 we can notice that I can multiply them together, 11 right, by doing X plus three times X minus three. 12 And if I were to do that, I would actually be getting this, 13 uh, this denominator right here. So I'm going to start rewriting arc 14 our equation minus nine. 15 But when I get to this fraction here with the X plus three, 16 I'm going to actually multiply it by X minus three on the top. 17 And the bottom. 18 We'll see that if I were to foil this out, 19 I get X squared minus nine. So I'll now rewrite it so that they 20 have a common denominator. And I'll also, 21 um, distribute the two X the simplify, 22 which will give me two X squared, minus six X. 23 We can now erase this and drop this down into my numerator. 24 And so now I'm on the road to simplifying this expression so that we 25 have a common denominator and I can do the same thing. 26 On the other side, I have one over X squared, 27 minus three, but I'll now multiply this by X plus three, 28 ...