SOLUTION: I'm having trouble with this fraction. 1-8r^3 ________ 8r^2+4r+2

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Question 185809This question is from textbook Beginning and Intermediate Algebra
: I'm having trouble with this fraction.

1-8r^3
________
8r^2+4r+2 This question is from textbook Beginning and Intermediate Algebra

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%281-8r%5E3%29%2F%288r%5E2%2B4r%2B2%29 Start with the given expression


%28%281-2r%29%281%2B2r%2B4r%5E2%29%29%2F%288r%5E2%2B4r%2B2%29 Factor the numerator using the difference of cubes formula A%5E3-B%5E3=%28A-B%29%28A%5E2%2BAB%2BB%5E2%29


%28%281-2r%29%281%2B2r%2B4r%5E2%29%29%2F%282%284r%5E2%2B2r%2B1%29%29 Factor the GCF 2 from the denominator.


%28%281-2r%29%284r%5E2%2B2r%2B1%29%29%2F%282%284r%5E2%2B2r%2B1%29%29 Rearrange the terms in the numerator in descending order.


Highlight the common terms.


Cancel out the common terms.


%281-2r%29%2F2 Simplify


So %281-8r%5E3%29%2F%288r%5E2%2B4r%2B2%29 simplifies to %281-2r%29%2F2


In other words, %281-8r%5E3%29%2F%288r%5E2%2B4r%2B2%29=%281-2r%29%2F2