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angelwings996

  • 2 years ago

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

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

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

  4. phi
    • 2 years ago
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    are you posting one of the multiple choices ?

  5. angelwings996
    • 2 years ago
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    This isn't a multiple choice problem

  6. phi
    • 2 years ago
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    you have the wrong sign on 5x

  7. Hero
    • 2 years ago
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    Actually the numerator should be x^2 - 5x + 6

  8. angelwings996
    • 2 years ago
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    Okay, then what would I do?

  9. phi
    • 2 years ago
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    once you have a common denominator, you can combine the tops

  10. mathstudent55
    • 2 years ago
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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)

  11. mathstudent55
    • 2 years ago
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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).

  12. angelwings996
    • 2 years ago
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    Okay, I get you so far

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

  14. angelwings996
    • 2 years ago
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    Okay I did that

  15. mathstudent55
    • 2 years ago
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    |dw:1359654823726:dw|

  16. mathstudent55
    • 2 years ago
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    |dw:1359654885990:dw|

  17. angelwings996
    • 2 years ago
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    What did you do here?

  18. mathstudent55
    • 2 years ago
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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.

  19. angelwings996
    • 2 years ago
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    Ohh okay

  20. mathstudent55
    • 2 years ago
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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.

  21. mathstudent55
    • 2 years ago
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    Now combine like terms on the numerator.

  22. mathstudent55
    • 2 years ago
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    Then try factoring the numerator.

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

  24. mathstudent55
    • 2 years ago
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    Correct. The last step is to try to factor the numerator to see if you can simplify the fraction.

  25. angelwings996
    • 2 years ago
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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

  26. mathstudent55
    • 2 years ago
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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.

  27. angelwings996
    • 2 years ago
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    Okay, What would the restrictions be then ? @mathstudent55

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

  29. mathstudent55
    • 2 years ago
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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.

  30. angelwings996
    • 2 years ago
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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

  31. angelwings996
    • 2 years ago
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    Or would I put x^2 - 9 as the denominator ?

  32. mathstudent55
    • 2 years ago
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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.

  33. angelwings996
    • 2 years ago
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    Okay, thank you so much for your help ! (:

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