SOLUTION: Reduce the given complex fraction into simple fraction. (a-2/a+2) + (a-2) / (a) - (3a+12/a+2)

Algebra ->  Exponents-negative-and-fractional -> SOLUTION: Reduce the given complex fraction into simple fraction. (a-2/a+2) + (a-2) / (a) - (3a+12/a+2)      Log On


   

Question 198535: Reduce the given complex fraction into simple fraction. (a-2/a+2) + (a-2) / (a) - (3a+12/a+2)
Answer by Edwin McCravy(20059) About Me  (Show Source):
You can put this solution on YOUR website!

%28%28a-2%29%2F%28a%2B2%29+%2B+%28a-2%29%29+%2F+%28a+-+%283a%2B12%29%2F%28a%2B2%29%29

Put a 1 under the %28a-2%29 in the top and
under the a on the bottom so everything
will be a fraction:



Enclose every fraction within parentheses:



Since the LCD for all four fractions top and bottom
is %28a%2B2%29, multiply top and bottom by %28a%2B2%29
written as %28%28a%2B2%29%2F1%29



Cancel the %28a%2B2%29's in two places:



Ignoring all the 1 denominators, all we have
left is



Use FOIL to change %28a%2B2%29%28a-2%29 to a%5E2-2a%2B2a-4 
to a%5E2-cross%282a%29%2Bcross%282a%29-4 to a%5E2-4
and multiply out the bottom:




%0D%0A%28%0D%0Aa-2%2Ba%5E2-4%0D%0A%29%0D%0A%2F%0D%0A%28%0D%0Aa%5E2-a-12%0D%0A%29%0D%0A

%0D%0A%28%0D%0Aa%5E2%2Ba-6%0D%0A%29%0D%0A%2F%0D%0A%28%0D%0Aa%5E2-a-12%0D%0A%29%0D%0A

Factor the numerator and denominator:

%28%0D%0A%28a%2B3%29%28a-2%29%0D%0A%29%2F%0D%0A%28%0D%0A%28a-4%29%28a%2B3%29%29%0D%0A

Cancel the %28a%2B3%29's



All that's left is

%28a-2%29%2F%28a-4%29

Edwin