Explanation for Question 29 From the Math (Calc) Section on the 2019 March Sat
Question 29 says the equation above is true for all values where X is 2 greater than two, where R and T are positive constants. 3 What is the value of our times? T so just start with this problem. 4 I'm just going to take the left side of this equation and I'm going 5 to do this addition. So we have two over X minus two, 6 plus three, over X plus five. 7 So to add these together, we're going to have to multiply this side of 8 the fraction by X plus five, over X plus five. 9 And this side by X minus two, 10 over X minus two. And that gives us X plus five 11 times two plus three X minus 12 two is over X plus five 13 X minus two. And so from that, 14 because this is equal to RX plus T over X minus two X 15 plus five. Now, 16 since both sides of the fraction are both sides of the equation have the 17 same denominator. 18 We can actually cancel out the denominators and just set the numerators equal to 19 each other. So I'm going to do that here. 20 So that's how we have this set up right now. Now we're going to 21 distribute. So two times X plus five is two X 22 plus 10, and then we're going to add that to three X plus negative 23 six, and that's equal to our X plus T. 24 And then finally we can add and subtract like terms and we get five 25 X plus four is equal to R X plus 26 T. So now we can see that five is equal to R so 27 R is equal to five, and that T is equal to four. 28 So the value of our tents T it's just five times four, 29 which is 20. So we know that the answer is.