Explanation for Question 17 From the Math (No Calc) Section on the 2018 March Sat
Question 17 asks what value of X satisfies the equation above. 2 So to add and subtract like terms here, 3 we're going to actually have to modify these fractions. 4 We need them to have the same denominator. 5 So I'm going to multiply this first part by X minus one, 6 over X minus one. And this second fraction by X 7 over X. And that's going to give us X minus one over 8 X squared, minus X, plus X over X 9 squared minus X. And that can be rewritten as X plus 10 X minus one, over X squared, 11 minus X. And then if we add and subtract like terms, 12 we get two X minus one over X squared, 13 minus X is equal to zero. 14 We can multiply both sides by X squared, 15 minus X, and we get to ax minus one is equal 16 to zero. Then we can add one to both sides, 17 which gives us two X, two 18 X is equal to one and then divide both sides by two. 19 And we get X is equal to one half. 20 And that's the correct answer to question 17 one half.