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← Complex Fractions Practice 3 - Visualizing Algebra

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Showing Revision 2 created 05/25/2016 by Udacity Robot.

  1. 1 divided by 9axy is correct. You're becoming a pro at these complex fractions
  2. if you got this one correct. The lowest common denominator might have been
  3. tricky, so let's find that first. We look at the denominators of 3 a squared b,
  4. and ab. We know these two denominators share a common factor of a times b. The
  5. other factor for this denominator is 3a. And the other factor for this
  6. denominator is 1. We multiply them together to get 3 times a squared times b.
  7. And remember we want the highest power of any variable or factor that appears in
  8. our denominators, 3 is the highest number factor, a squared is the highest
  9. variable factor for a And 1b or just b is the highest for, well b. Next we
  10. multiply by the LCD divided by LCD a form of one. These two factors would cancel
  11. out, leaving us with 2xy in the numerator. Here we can cancel out 1a and 1b.
  12. This means we have to drop this power down by one. Leaving us with 3a times this
  13. expression. 3 times 6 is 18 and then we just list the product of the variables.
  14. Now you might be wondering why I listed this a first instead of on the end.
  15. Usually we list the product of the variables in alphabetical order but it's
  16. certainly okay to leave this a on the end. And finally we want to simplify our
  17. rational expression. These are the factors of the numerator. And these are the
  18. factors of the denominator. We can cancel the factors that equal 1, which leaves
  19. us with a 1 in the numerator and 9 times a times x times y, in our denominator.
  20. This is why it's important to remember that 2 divided by 2 equals 1. There's
  21. still a 1 in our numerator. We want to make sure that appears in our answer. We
  22. can't simplify this anymore, since 1 is the only factor in our numerator so
  23. we're completely done.