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← Equivalent Fractions Rational Expressions - Visualizing Algebra

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

  1. We multiply this first fraction by p plus 3 divided by p plus 3. The denominator
  2. here is missing a factor of p plus 3. This is the one factor we need in order to
  3. change our denominator into the LCD. For our second fraction we multiply by p
  4. minus 1 divided by p minus 1. And this denominator, p minus 1 is the missing
  5. factor we need in order to get the LCD. Now we multiply these two numerators
  6. together and these two denominators together this gives us our new first
  7. equivalent fraction. We do the same process for the second fraction to get this,
  8. these two denominators may look different but they really the same. We know the
  9. order of the factors don't matter because its multiplication. Now that the two
  10. fractions have like denominators, we can simply add the numerators together. We
  11. add the like terms. The p's and the constants. 1 p and 1 p would equal 2 p and
  12. positive 3 and negative 1 would equal positive 2. Now that we're here, we should
  13. ask ourselves, are we done? Well, we added two things in a numerator together,
  14. so we have a new numerator entirely. We want to see if we can factor it if
  15. possible, and it turns out we can. We can take out a 2, to have 2 times p plus
  16. 1. But this doesn't really help us. We can't cancel a factor of p plus 1 since
  17. another factor of p plus 1 does not appear in the denominator. So the answer is
  18. yes, we're done, and here's the addition of these two rational expressions. Now
  19. this is some algebra.