SOLUTION: Hi, I need help solving this problem on reducing rational expressions: {{{((a^2-4ab+4b^2)-z^2)/(5a-10b+5z)}}} Thanks!

Algebra ->  Rational-functions -> SOLUTION: Hi, I need help solving this problem on reducing rational expressions: {{{((a^2-4ab+4b^2)-z^2)/(5a-10b+5z)}}} Thanks!      Log On


   



Question 108232: Hi, I need help solving this problem on reducing rational expressions:
%28%28a%5E2-4ab%2B4b%5E2%29-z%5E2%29%2F%285a-10b%2B5z%29
Thanks!

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
Hi, I need help solving this problem on reducing rational expressions:
%28%28a%5E2-4ab%2B4b%5E2%29-z%5E2%29%2F%285a-10b%2B5z%29
Thanks!

%28%28a%5E2-4ab%2B4b%5E2%29-z%5E2%29%2F%285a-10b%2B5z%29

Factor the %28a%5E2-4ab%2B4b%5E2%29 as %28a-2b%29%28a-2b%29 which
can be written as %28a-2b%29%5E2. So now we have

%28%28a-2b%29%5E2-z%5E2%29%2F%285a-10b%2B5z%29

Now the numerator is the difference of two squares, 
which factors as
[%28a-2b%29-z][%28a-2b%29%2Bz] or
[a-2b-z][a-2b%2Bz] or
%28a-2b-z%29%28a-2b%2Bz%29.  So now we have:

+%28%28a-2b-z%29%28a-2b%2Bz%29%29+%2F%285a-10b%2B5z%29

Now we factor the denominator simply by taking out 5, and so
we now have

+%28%28a-2b-z%29%28a-2b%2Bz%29%29+%2F%285%28a-2b%2Bz%29%29

Now we can cancel the %28a-2b%2Bz%29's and all that's left is

+%28a-2b-z%29+%2F5

Edwin