Thread for Week 3 - Discussion Question #1 Take any number (except for 1). Square that number and then subtract one. Divide by one less than your original number. Now subtract your original number. Did you reached 1 for an answer? You should have. How do

Suppose we take the number 5 Squaring 5^2 = 5*5 = 25 Subtracting 1 25 -1 = 24 Dividing by 1 less means 5-1 = 4 24/4 = 6 Subtracting original number 6 – 5 = 1 Yes answer is 1. Taking variable y Squaring y^2 Subtracting 1 y^2 -1 Dividing by 1 less means y^2-1 / (y-1) = (y+1)(y-1)/(y-1) = y+1 Subtracting original number y+1 - y = 1 Yes answer is 1.   Here is a number game that uses the skills of simplifying rational expressions. Take any number (except for -4) and add 2. Next, multiply by 2 less than the number. Add 3 times the original number. Divide by 4 more than the original number. Finally, add 1. You should be back where you started! Here it is with symbols: Take any number (except for -4) and add 2. x x+2 Next, multiply by 2 less than the number. (x+2)(x-2) = x^2 - 4 Add 3 times the original number. x^2 + 3x - 4 = (x+4)(x-1) Divide by 4 more than the original number. (x+4)(x-1)/(x+4) = x-1 Finally, add 1. You should be back where you started!