SOLUTION: {{{(2u^(-1) - w^(-1))/(4u^(-2) - w^(-2))}}}

Algebra ->  Trigonometry-basics -> SOLUTION: {{{(2u^(-1) - w^(-1))/(4u^(-2) - w^(-2))}}}      Log On


   

Question 1144941: %282u%5E%28-1%29+-+w%5E%28-1%29%29%2F%284u%5E%28-2%29+-+w%5E%28-2%29%29
Answer by Edwin McCravy(20059) About Me  (Show Source):
You can put this solution on YOUR website!
%282u%5E%28-1%29+-+w%5E%28-1%29%29%2F%284u%5E%28-2%29+-+w%5E%28-2%29%29

%282%281%2Fu%29+-+1%2Fw%29%2F%284%281%2Fu%5E2%29+-+w%5E2%29%29

%282%2Fu-1%2Fw%5E%22%22%29%2F%284%2Fu%5E2-1%2Fw%5E2%29

The LCD of all 4 denominators, top and bottom is u²w².
Multiply every term top and bottom by u²w² (put it over 1 so
everything will be a fraction, and it'll be easier to see:




Then we cancel what will cancel:



And we have no fractions on the top or bottom:

%282uw%5E2-u%5E2w%29%2F%284u%5E2-u%5E2%29

We factor out uw on top, and factor the bottom as the difference
of squares:

%28uw%282w-u%29%29%2F%28%282w-u%29%282w%2Bu%29%29

Finally we cancel the (2w-u)'s

%28uw%28cross%282w-u%29%29%29%2F%28%28cross%282w-u%29%29%282w%2Bu%29%29

And the final answer is:

%28uw%29%2F%282w%2Bu%29

Edwin