SOLUTION: {{{(2-x/y)/(1/y+y)}}}

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Question 78035: %282-x%2Fy%29%2F%281%2Fy%2By%29
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!

%282-x%2Fy%29%2F%281%2Fy%2By%29

Write the 2 over 1} and the y over 1
so the whole "building" will be 4 "stories"
high.

%282%2F1-x%2Fy%29%2F%281%2Fy%2By%2F1%29

Put parentheses around the numerator and the
denominator:

%28%282%2F1-x%2Fy%29%29%2F%28%281%2Fy%2By%2F1%29%29

Look at all four denominators, 1,y,y,and 1
Their LCD is y. So multiply by y%2Fy
which just equals 1. But make it four "stories" 
high also by putting each of the y's over
1 like this

%28y%2F1%29%2F%28y%2F1%29

Now since this just equals to 1, we can multiply
it by our example without changing its value.

%28y%2F1%29%2F%28y%2F1%29%28%282%2F1-x%2Fy%29%29%2F%28%281%2Fy%2By%2F1%29%29 

Now remove the parentheses by distributing:



The first term on top just becomes 2y%2F1 which is
just 2y

%28+2y-%28y%2F1%29%28x%2Fy%29+%29%2F%28+%28y%2F1%29%281%2Fy%29%2B%28y%2F1%29%28y%2F1%29+%29

The y's cancel in the second term on top, leaving
just x%2F1 which is just x

%28+2y-x%29%2F%28+%28y%2F1%29%281%2Fy%29%2B%28y%2F1%29%28y%2F1%29+%29

The y's cancel in the first term on the bottom,
leaving 1%2F1 which is just 1

%28+2y-x%29%2F%28+1%2B%28y%2F1%29%28y%2F1%29+%29

Finally the second term on the bottom becomes y%5E2%2F1
which is just y%5E2 and so we end up with just

%28+2y-x%29%2F%28+1%2By%5E2+%29

Edwin