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← Add Rational Expressions Practice 2 - Visualizing Algebra

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

  1. This was our final answer. Excellent work if you found it. We start by finding
  2. the lowest common denominator, which means that we have to factor this
  3. denominator and this one first. Factors of 24 that sum to positive 10 are
  4. positive 6 and positive 4, while the factors of negative 12 that sum to positive
  5. 1 are positive 4 and negative 3. This means that our lowest common denominator
  6. would be y plus 6 times y plus 4 times y minus 3. Next, we multiply each
  7. fraction by the missing factors of our lowest common denominator. For the first
  8. denominator, it's missing the factor y minus 3. So we multiply the numerator and
  9. denominator by y minus 3, since we're really just multiplying by 1. For the
  10. second fraction, we need to multiply by y plus 6 divided by y plus 6. When we
  11. multiply each of these fractions by a form of 1, we get two new equivalent
  12. fractions. We multiply these two numerators together, or these two binomials
  13. together, to get y squared minus 6y plus 9. And then here again, we multiply
  14. these two binomials together to get y squared plus 12y plus 36. We multiply
  15. these out, since we're adding our numerators in the end. The denominators,
  16. however, we can just leave in factored form since these won't change. When we
  17. add the like terms of our numerators together, we get 2y squared from 1y squared
  18. and 1y squared. We get positive 6y, from negative 6y and positive 12y. And we
  19. get 45 from positive 9 and positive 36. And finally, we want to check to see if
  20. this is factorable, to see if we can cancel a factor in the numerator and
  21. denominator. We find factors of 90 that sum to positive 6. When I look at the
  22. positive factors of 90, these are the factor pairs. None of these add to
  23. positive 6. So I know this numerator is not factorable. Since we cant factor
  24. this numerator, we actually have our final answer. None of these add to positive
  25. 6.