Explanation for Question 12 From the Math (No Calc) Section on the Official Sat Practice Test 9
Question 12 gives us this expression and it asks us, 2 which of the following is equivalent to the expression above for X is greater 3 than zero. Okay. 4 So looking at these answer choices, one thing that we notice is that they 5 all have a common denominator and our expression does not. 6 So what we're going to want to do is we're going to want to 7 try and find a common denominator, meaning that the whole thing will be over 8 two X plus one. In order to do that, 9 let's write this out bigger at the bottom. We have one over 10 two X plus one plus five, 11 and let's just look at this five isolated for now. 12 We want the denominator to be two X minus two X plus one, 13 excuse me. And in order to do that, 14 we can multiply both the top and the bottom by two X plus 15 one. 16 And in multiplying both the numerator and the denominator by two X plus one, 17 that's how we make sure that it has the same meaning because you could 18 just simplify it out and get five still. 19 But we want the convention to be that the denominator is two explosive one. 20 So this expression is now equivalent to the 21 expression above. We have one of our two exposed one plus five of her, 22 five times two X plus one over two X plus one. 23 Now what we can do is we can combine the denominators so 24 we can just add the numerators of the dome. Denominators are the same. 25 So we have one plus five times, 26 two X plus one over the common denominator of two X 27 plus one. And now we're just going to simplify out. 28 So we have one plus five times two X is equal to 10 X 29 and then five times one is going to be equal to five solving 30 through. We have six. 31 So one plus five is equal to six plus 10 X over two 32 X plus one. And that is the answer that 33 we're left with six plus 10 X over two X plus one. 34 Let's go back into the answer choices and see if that's reflected anywhere. 35 And we do have that with answer choice D so 10 X plus six, 36 over two X plus one is D.