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angelwings996 Group Title

Algebra 2 help please!? Simplify the sum. State any restrictions on the variables.

  • one year ago
  • one year ago

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  1. angelwings996 Group Title
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    • one year ago
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  2. Hero Group Title
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    Hint: Multiply the first fraction by (x - 3)/(x-3)

    • one year ago
  3. angelwings996 Group Title
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    so would it become \[\frac{ x ^{2} + 5x + 6 }{ x ^{2} - 9 }\] @Hero

    • one year ago
  4. phi Group Title
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    are you posting one of the multiple choices ?

    • one year ago
  5. angelwings996 Group Title
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    This isn't a multiple choice problem

    • one year ago
  6. phi Group Title
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    you have the wrong sign on 5x

    • one year ago
  7. Hero Group Title
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    Actually the numerator should be x^2 - 5x + 6

    • one year ago
  8. angelwings996 Group Title
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    Okay, then what would I do?

    • one year ago
  9. phi Group Title
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    once you have a common denominator, you can combine the tops

    • one year ago
  10. mathstudent55 Group Title
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    Since you are adding fractions, you need a common denominator. The denominator of the left fraction is simply x + 3. You need to factor the denominator of the right fraction. x^2 - 9 = (x + 3)(x - 3)

    • one year ago
  11. mathstudent55 Group Title
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    Since the right denominator has factors (x + 3)(x - 3) and the left fraction only has (x + 3), you need to multiply the numerator and denominator of the left fraction by (x - 3).

    • one year ago
  12. angelwings996 Group Title
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    Okay, I get you so far

    • one year ago
  13. mathstudent55 Group Title
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    Then multiply out the numerator of the left fraction (x + 3)(x - 2)

    • one year ago
  14. angelwings996 Group Title
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    Okay I did that

    • one year ago
  15. mathstudent55 Group Title
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    |dw:1359654823726:dw|

    • one year ago
  16. mathstudent55 Group Title
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    |dw:1359654885990:dw|

    • one year ago
  17. angelwings996 Group Title
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    What did you do here?

    • one year ago
  18. mathstudent55 Group Title
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    Since both fractions now have the same denominator, you can write them as a single fraction over the common denominator. Now combine like terms in the numerator.

    • one year ago
  19. angelwings996 Group Title
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    Ohh okay

    • one year ago
  20. mathstudent55 Group Title
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    I multiplied out the left numerator and I added the right numerator, and set the whole thing over the common denominator.

    • one year ago
  21. mathstudent55 Group Title
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    Now combine like terms on the numerator.

    • one year ago
  22. mathstudent55 Group Title
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    Then try factoring the numerator.

    • one year ago
  23. angelwings996 Group Title
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    When I combine like terms I got \[\frac{ x ^{2} + 11x - 6 }{ (x+3)(x-3) }\]

    • one year ago
  24. mathstudent55 Group Title
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    Correct. The last step is to try to factor the numerator to see if you can simplify the fraction.

    • one year ago
  25. angelwings996 Group Title
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    I can't figure out how to factro this, nothing I can find will come up with both 11 and 6

    • one year ago
  26. mathstudent55 Group Title
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    This kind of factoring involves finding two numbers that multiply to -6 and add to 11. There aren't any, so it can't be factored, and the addition is finished.

    • one year ago
  27. angelwings996 Group Title
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    Okay, What would the restrictions be then ? @mathstudent55

    • one year ago
  28. angelwings996 Group Title
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    Would the answer be with the denominator factored or can I put x^2 - 9 ?

    • one year ago
  29. mathstudent55 Group Title
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    The restrictions are any values of x that would make the denominator zero. Since the denominator is x^2 - 9 which you know factors into (x + 3)(x - 3), set x + 3 = 0 and solve for x and set x - 3 = 0 and solve for x. Those two x values are the restrictions.

    • one year ago
  30. angelwings996 Group Title
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    Okay thank you..so the answer woould be \[\frac{ x ^{2} + 11x - 6 }{ (x + 3)(x - 3) } ; x \neq -3, 3\] @mathstudent55

    • one year ago
  31. angelwings996 Group Title
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    Or would I put x^2 - 9 as the denominator ?

    • one year ago
  32. mathstudent55 Group Title
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    You can leave the denominator factored. It's perfectly acceptable. It's also fine to multiply it out. Either way is good.

    • one year ago
  33. angelwings996 Group Title
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    Okay, thank you so much for your help ! (:

    • one year ago
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