SOLUTION: Can you help me simplify this expression, using only positive exponents in the answer...I don't quite understand these, so if you could be detailed, I would appriciate it. {{{(a

Algebra ->  Functions -> SOLUTION: Can you help me simplify this expression, using only positive exponents in the answer...I don't quite understand these, so if you could be detailed, I would appriciate it. {{{(a      Log On


   

Question 122902: Can you help me simplify this expression, using only positive exponents in the answer...I don't quite understand these, so if you could be detailed, I would appriciate it.
%28a%5E-2-4b%5E-2%29%2F%283b-6a%29
Found 2 solutions by jim_thompson5910, ankor@dixie-net.com:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28a%5E-2-4b%5E-2%29%2F%283b-6a%29 Start with given expression


%281%2Fa%5E2-4%2Fb%5E2%29%2F%283b-6a%29 Flip the bases that have negative exponents. Remember a%5E-2=1%2Fa%5E2

%28%28b%5E2%2Fb%5E2%29%281%2Fa%5E2%29-%28a%5E2%2Fa%5E2%29%284%2Fb%5E2%29%29%2F%283b-6a%29 Multiply the first fraction 1%2Fa%5E2 by b%5E2%2Fb%5E2. Multiply the second fraction 1%2Fb%5E2 by a%5E2%2Fa%5E2.


%28%28b%5E2%29%2F%28a%5E2b%5E2%29-%284a%5E2%29%2F%28a%5E2b%5E2%29%29%2F%283b-6a%29 Multiply the fractions


%28%28b%5E2-4a%5E2%29%2F%28a%5E2b%5E2%29%29%2F%283b-6a%29 Combine the fractions in the numerator



%28%28b%5E2-4a%5E2%29%2F%28a%5E2b%5E2%29%29%2A%281%2F%283b-6a%29%29 Multiply the first fraction by the reciprocal of the second fraction



%28%28%28b%2B2a%29%28b-2a%29%29%2F%28a%5E2b%5E2%29%29%2A%281%2F%283%28b-2a%29%29%29 Factor b%5E2-4a%5E2 to get %28b%2B2a%29%28b-2a%29. Factor 3b-6a to get 3%28b-2a%29



Cancel like terms



%28b%2B2a%29%2F%283a%5E2b%5E2%29 Simplify



Answer:


So %28a%5E-2-4b%5E-2%29%2F%283b-6a%29 simplifies to %28b%2B2a%29%2F%283a%5E2b%5E2%29


In other words, %28a%5E-2-4b%5E-2%29%2F%283b-6a%29=%28b%2B2a%29%2F%283a%5E2b%5E2%29

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):