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← The Different Expression 3 - Visualizing Algebra

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

  1. We can see that these two rational expressions are equal. If we switch the order
  2. of the terms in the numerator of this expression, we'll get x plus 9 divided by
  3. the quantity x minus 9. Now we need to decide between these two expressions. We
  4. can switch the order of the terms in the numerator and in the denominator. The x
  5. stays negative here and the 9 stays positive. For this expression, we don't want
  6. to switch the order of the numerator, since it's already x plus 9. It matches
  7. the other ones. And here's where this negative sign comes in handy. We can
  8. distribute this negative sign to each term in the numerator, or to each term in
  9. the denominator. I'm going to multiply our denominator by negative 1. Negative 1
  10. times 9 is negative 9. And negative 1 times negative x is positive x. Finally,
  11. we commute this edition to get x plus 9, divided by the quantity x minus 9. So
  12. we know this rational expression is equal to these two. This one is definitely
  13. different.