Hi everyone! This is my first post on SDN so apologies if this is the wrong place or any formatting is weird, etc. I saw a thread from 2011 on the same problem, but the solution to the question (Math Destroyer 2015 - Test 12 - Question 28) is confusing to me.
The question asks to simplify the equation, which is 1 - (1/[1+a/1-a]). In the red ink is the solution from the old SDN post (Destroyer doesn't have an explanation). What the person did was simplify the fraction in the denominator by multiplying the top and bottom by the term (1-a). That makes sense conceptually to me (as does the rest of the problem with the plugging back in), but what I don't really understand is when one multiplies the bottom term (1+a)/(1-a) times (1-a), doesn't that essentially cancel out, leaving 1+a on the bottom? Where does the (1-a)+a come from? Sorry if this is confusing. I would greatly appreciate any help on this! Thank you 🙂
The question asks to simplify the equation, which is 1 - (1/[1+a/1-a]). In the red ink is the solution from the old SDN post (Destroyer doesn't have an explanation). What the person did was simplify the fraction in the denominator by multiplying the top and bottom by the term (1-a). That makes sense conceptually to me (as does the rest of the problem with the plugging back in), but what I don't really understand is when one multiplies the bottom term (1+a)/(1-a) times (1-a), doesn't that essentially cancel out, leaving 1+a on the bottom? Where does the (1-a)+a come from? Sorry if this is confusing. I would greatly appreciate any help on this! Thank you 🙂
