SOLUTION: ((a/(x+y))+(m/y))/(x/(a+m))

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Question 151383: ((a/(x+y))+(m/y))/(x/(a+m))
Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28%28a%2F%28x%2By%29%29%2B%28m%2Fy%29%29%2F%28x%2F%28a%2Bm%29%29 Start with the given expression.


Multiply every term by the LCD y%28x%2By%29%28a%2Bm%29 to clear the inner denominators.



%28y%28a%2Bm%29%28a%29%2B%28x%2By%29%28a%2Bm%29%28m%29%29%2F%28y%28x%2By%29%28x%29%29 Simplify


%28ay%28a%2Bm%29%2Bm%28x%2By%29%28a%2Bm%29%29%2F%28xy%28x%2By%29%29 Rearrange the terms.


%28ay%28a%2Bm%29%2Bm%28ax%2Bmx%2Bay%2Bmy%29%29%2F%28xy%28x%2By%29%29 FOIL


%28a%5E2y%2Bamy%2Bamx%2Bm%5E2x%2Bamy%2Bm%5E2y%29%2F%28x%5E2y%2Bxy%5E2%29 Distribute


%28a%5E2y%2Bamx%2Bm%5E2x%2B2amy%2Bm%5E2y%29%2F%28x%5E2y%2Bxy%5E2%29 Combine like terms.


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Answer:


So %28%28a%2F%28x%2By%29%29%2B%28m%2Fy%29%29%2F%28x%2F%28a%2Bm%29%29 simplifies to %28a%5E2y%2Bamx%2Bm%5E2x%2B2amy%2Bm%5E2y%29%2F%28x%5E2y%2Bxy%5E2%29

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
((a/(x+y))+(m/y))/(x/(a+m))
----------------------------
Simplifying the numerator:
((a/(x+y))+(m/y))
lcd = y(x+y)
(ay + m(x+y)/y(x+y)
((a+m)y + mx)/(y(x+y))
------------------------
Inverts the denominator and multiply:
((a+m)y + mx)/(y(x+y)) * (a+m)/x
= [(a+m)^2 y + mx(a+m)] / [xy(x+y)]
--------------
That doesn't look any better than the original expression but
it does have one numerator and one denominator.
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Cheers,
Stan H.