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← Subtract Rational Expressions Practice 2 - Visualizing Algebra

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Showing Revision 5 created 05/24/2016 by Udacity Robot.

  1. To subtract the second rational expression we really want to add the opposite.
  2. We want to distribute our subtraction sign to each term in the numerator which
  3. gives us a negative 1. Now we factor each denominator and try to find the lowest
  4. common denominator between the two fractions. The lowest common denominator is x
  5. minus 1 times x minus 1 times x plus 1. We know this since these two
  6. denominators share a common factor of x minus 1. The other factor for this
  7. denominator is x minus 1. And the other factor for this denominator is x plus 1.
  8. We multiply each fraction by the missing factors of the lowest common
  9. denominator. For the first fraction, we distribute 6x to the quantity x plus 1.
  10. We'll get 6x squared plus 6x. For this second fraction, we'll have negative 1
  11. times the quantity x minus 1. We really just changed these two signs. So we'll
  12. have negative x plus 1. Now that we have two fractions with common denominators
  13. We can add the numerators together. We just add the like terms. When we add the
  14. like terms of 6x and negative x together we'll get 6x squared plus 5x plus 1.
  15. Now remember, we have a new numerator here. And let's see if we can factor it.
  16. We want factors of positive 6 that's sum to 5. Well yes that would be 3 and 2.
  17. This would be the factored form if we use factoring by grouping. But notice that
  18. this doesn't help us out. None of these factors appears in our denominator. We
  19. can't simply any more. I final answer would be 6 x squared plus 5 x plus 1.
  20. Divided by the factors of this denominator.