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← Simplify Rational Expressions Practice 3 - Visualizing Algebra

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

  1. Here's our answer. Great work if you got that one correct. We can factor the
  2. numerator to be x plus 3 times x minus 3, since this is the difference of two
  3. squares. Our denominator factors into x plus 3 squared. This is a perfect square
  4. trinomial. The first term is a square. The second term is a square, and the
  5. middle terms is twice the square root of the first term and the last term. We
  6. know for the square exponent, we really write this factor twice. From here, it's
  7. easy to see we have a common factor of x plus 3, in the numerator and the
  8. denominator. So those simplify to equal 1. Another way to think about
  9. simplifying this is to do it over here. We have an exponent of 1 for this x plus
  10. 3. An exponent of 2 for this x plus 3. We use one of these x plus 3s to cancel
  11. with the 1 and the numerator. So our power of 2 drops down to a power of 1 and
  12. we lose this factor altogether. Keep in mind that things aren't equal in 0 here,
  13. it's really that we have an equivalence of 1, x plus 3 divided by x plus 3. This
  14. leaves us with our final answer.