SOLUTION: simplify the expression: (1/(.5x+y) − 2y/(.25x2+xy+y2))÷(.5x/(.25x2−y2) + 1/(2y−x))+2

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Question 1132474: simplify the expression:
(1/(.5x+y) − 2y/(.25x2+xy+y2))÷(.5x/(.25x2−y2) + 1/(2y−x))+2

Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!
Is this what you meant?:



Change all the decimals to common fractions:



Factor out the common fractions:

Factor 




Factor 

 



  
Factor 

 



Substitute those:


       
Multiply top and bottom of the upper left fraction in large
parentheses by 2.

Multiply top and bottom of the upper right fraction in large
parentheses by 4.

Multiply top and bottom of the lower left fraction in large
parentheses by 4.


       
Multiply the 2 by the 4 in the top right, and the 1/2 by the 4 in
the bottom left and there are no more common fractions, just
algebraic fractions:



Notice that all the expressions except 2y-x have x appearing first 
and y appearing second.  Lets change the bottom right fraction so that
x appears before y:









So we have:



The LCD of all the 4 algebraic fractions in the compound
fraction is (x-2y)(x+2y)²

We multiply ever term in the top and bottom by (x-2y)(x+2y)²
placing it over 1






Then we cancel:





Factor 2(x-2y) out of the top and (x+2y) out of the bottom:











Now we multiply the +2 by 





Write the sum of the numerators over the common denominator:







Whew! :)

Edwin

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