SOLUTION: how do i do this? Simplify the following fraction by putting it in lowest terms or by performing the indicated operation. {{{(a^3-b^3)/(a^3b^3+a^2b^4+ab^5)}}}

Algebra ->  Rational-functions -> SOLUTION: how do i do this? Simplify the following fraction by putting it in lowest terms or by performing the indicated operation. {{{(a^3-b^3)/(a^3b^3+a^2b^4+ab^5)}}}      Log On


   

Question 146272: how do i do this? Simplify the following fraction by putting it in lowest terms or by performing the indicated operation.
%28a%5E3-b%5E3%29%2F%28a%5E3b%5E3%2Ba%5E2b%5E4%2Bab%5E5%29
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
how do i do this? Simplify the following fraction by putting it in lowest terms or by performing the indicated operation. 

%28a%5E3-b%5E3%29%2F%28a%5E3b%5E3%2Ba%5E2b%5E4%2Bab%5E5%29

Factor the top as the difference of two cubes, using this rule:

FIRST%5E3-SECOND%5E3=%28FIRST-SECOND%29%28FIRST%5E2%2BFIRST%2ASECOND%2BSECOND%5E2%29

%28%28a-b%29%28a%5E2%2Bab%2Bb%5E2%29%29%2F%28a%5E3b%5E3%2Ba%5E2b%5E4%2Bab%5E5%29

Factor the bottom by taking out GCF ab%5E3:

%28%28a-b%29%28a%5E2%2Bab%2Bb%5E2%29%29%2F%28ab%5E3%28a%5E2%2Bab%2Bb%5E2%29%29

Now we cancel the %28a%5E2%2Bab%2Bb%5E2%29's



and we are left with

%28a-b%29%2F%28ab%5E3%29

Edwin