## ← Divide Rational Expressions 6 - Visualizing Algebra

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Showing Revision 2 created 05/24/2016 by Udacity Robot.

1. We start our problem by multiplying by the reciprocal of our second fraction. We
2. flip it over. We can factor this first numerator as 5x plus 3 times 5x minus 3,
3. since this is the difference of two perfect squares. Our denominator is also a
4. difference of two perfect squares. So we have 2x plus 3 times 2x minus 3. For
5. this fraction, we can factor this numerator by finding the factors of negative
6. 18 that sum to negative 7. Those factors are negative 9 and positive 2. We use
7. factoring by grouping to get 3x plus 1 times 2x minus 3 for this first
8. numerator. And finally, for this denominator we find factors of positive 45 that
9. sum to negative 14. Those two factors are negative 9 and negative 5. These
10. factors let us rewrite our middle term, and then we can use factoring by
11. grouping. We get a denominator of 5x minus 3 times 3x minus 1. Now that we have
12. all of our factors, let's cancel factors that simplify to 1. These two factors
13. would reduce to 1, and these two factors would also reduce to 1, leaving us with
14. these factors for our answer. You're doing amazing at dividing rational
15. expressions and factoring if you got this one correct.