SOLUTION: how would i do this? Simplify the following fraction by putting it in lowest terms or by performing the indicated operation. 4x2-4x+1 over 8x3-1

Algebra ->  Numeric Fractions Calculators, Lesson and Practice -> SOLUTION: how would i do this? Simplify the following fraction by putting it in lowest terms or by performing the indicated operation. 4x2-4x+1 over 8x3-1      Log On


   

Question 146290: how would i do this? Simplify the following fraction by putting it in lowest terms or by performing the indicated operation.
4x2-4x+1 over 8x3-1
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%284x%5E2-4x%2B1%29%2F%288x%5E3-1%29 Start with the given expression.


%28%282%2Ax-1%29%5E2%29%2F%288x%5E3-1%29 Factor 4x%5E2-4x%2B1 to get %282%2Ax-1%29%5E2.


%28%282%2Ax-1%29%5E2%29%2F%28%282%2Ax-1%29%2A%284%2Ax%5E2%2B2%2Ax%2B1%29%29 Factor 8x%5E3-1 to get %282%2Ax-1%29%2A%284%2Ax%5E2%2B2%2Ax%2B1%29.



%28%282%2Ax-1%29%5Ecross%282%29%29%2F%28cross%282%2Ax-1%29%284%2Ax%5E2%2B2%2Ax%2B1%29%29 Cancel out the common terms.


%282%2Ax-1%29%2F%284%2Ax%5E2%2B2%2Ax%2B1%29 Simplify.


So %284x%5E2-4x%2B1%29%2F%288x%5E3-1%29 simplifies to %282%2Ax-1%29%2F%284%2Ax%5E2%2B2%2Ax%2B1%29.


In other words, %284x%5E2-4x%2B1%29%2F%288x%5E3-1%29=%282%2Ax-1%29%2F%284%2Ax%5E2%2B2%2Ax%2B1%29