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anonymous

  • one year ago

Classify the solutions of 3 over x plus 5, plus one fifth, equals 2 over x plus 5 as extraneous or non-extraneous.

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  1. anonymous
    • one year ago
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    @Algorithmic @ganeshie8 @CaptainLlama49

  2. anonymous
    • one year ago
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    is the answer extraneous?

  3. Mertsj
    • one year ago
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    I have typed this twice and lost it both times. I will try one more time.

  4. anonymous
    • one year ago
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    ok:)

  5. Mertsj
    • one year ago
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    \[\frac{3}{x+5}+\frac{1}{5}=\frac{2}{x+5}\]

  6. Mertsj
    • one year ago
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    Common denominator is 5(x+5). Multiply each term by that.

  7. anonymous
    • one year ago
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    so you get 15/5(x+5)+x+5/5(x+5)=10/5(x+5)

  8. Mertsj
    • one year ago
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    \[5(x+5)(\frac{3}{x+5})+5(x+5)(\frac{1}{5})=5(x+5)(\frac{3}{x+5})\]

  9. Mertsj
    • one year ago
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    Cancel all the denominators.

  10. Mertsj
    • one year ago
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    \[15 +x+5=10\]

  11. anonymous
    • one year ago
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    yup! :)

  12. Mertsj
    • one year ago
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    The 3 on the right side is supposed to be a 2

  13. Mertsj
    • one year ago
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    \[x=-10\]

  14. Mertsj
    • one year ago
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    Now. Is that extraneous or not? Does it cause any denominator to be 0? Does it make the original equation true?

  15. anonymous
    • one year ago
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    extraneous?

  16. Mertsj
    • one year ago
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    Why is it extraneous?

  17. anonymous
    • one year ago
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    3/ -5 +1/5 = 2/-5

  18. anonymous
    • one year ago
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    I don't know. When i plugged it in, that's the equation I got above,

  19. Mertsj
    • one year ago
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    \[-\frac{3}{5}+\frac{1}{5}=-\frac{2}{5}\]

  20. Mertsj
    • one year ago
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    Is that true or not?

  21. Mertsj
    • one year ago
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    Is any denominator equal to 0 ?

  22. anonymous
    • one year ago
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    no

  23. Mertsj
    • one year ago
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    Then it is a perfectly fine solution and is not extraneous.

  24. anonymous
    • one year ago
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    Oh!

  25. anonymous
    • one year ago
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    Thank you:)

  26. anonymous
    • one year ago
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    Can I ask one more?

  27. Mertsj
    • one year ago
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    An extraneous solution is a number that appears to be a solution but doesn't hold up to scrutiny because it either doesn't check or causes a denominator to be 0.

  28. Mertsj
    • one year ago
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    Yes

  29. anonymous
    • one year ago
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    Solve for x: 2 over 5 plus 3 over 5 x equals quantity x plus 5 over 10.

  30. anonymous
    • one year ago
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    Okay! I understand now:)

  31. anonymous
    • one year ago
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    For this one, I got x=-3,2

  32. Mertsj
    • one year ago
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    \[\frac{2}{5}+\frac{3}{5x}=\frac{x+5}{10}\]

  33. Mertsj
    • one year ago
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    Is that it?

  34. anonymous
    • one year ago
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    yeah:)

  35. Mertsj
    • one year ago
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    \[10x(\frac{2}{5})+10x(\frac{3}{5x})=10x(\frac{x+5}{10})\]

  36. Mertsj
    • one year ago
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    \[4x+6=x^2+5x\]

  37. anonymous
    • one year ago
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    -1x^2+5x+36

  38. Mertsj
    • one year ago
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    \[x^2+x-6=0\]

  39. Mertsj
    • one year ago
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    \[(x+3)(x-2)=0\]

  40. anonymous
    • one year ago
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    So, -3 and 2 ?

  41. Mertsj
    • one year ago
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    \[x=-3,2\]

  42. anonymous
    • one year ago
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    Last one:)?

  43. Mertsj
    • one year ago
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    \[\frac{2}{5}+\frac{3}{5(-3)}=\frac{-3+5}{10}\]

  44. Mertsj
    • one year ago
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    \[\frac{2}{5}-\frac{3}{15}=\frac{2}{10}\]

  45. Mertsj
    • one year ago
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    \[\frac{2}{5}-\frac{1}{5}=\frac{1}{5}\]

  46. Mertsj
    • one year ago
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    That seems to check. Try 2. See if it checks.

  47. anonymous
    • one year ago
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    Okay, that makes sense!! :D

  48. anonymous
    • one year ago
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    Classify the solutions of 1 over x plus 4, plus one half, equals 1 over x plus 4 as extraneous or non-extraneous.

  49. anonymous
    • one year ago
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    So, I got -4

  50. Mertsj
    • one year ago
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    \[\frac{1}{x+4}+\frac{1}{2}=\frac{1}{x+4}\]

  51. Mertsj
    • one year ago
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    And -4 causes the denominator to be 0 so it is extraneous.

  52. anonymous
    • one year ago
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    yes, I agree

  53. Mertsj
    • one year ago
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    Good job!!

  54. anonymous
    • one year ago
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    Solve for x: 1 over 2 plus 4 over 2 x equals quantity x plus 4 over 10.

  55. Mertsj
    • one year ago
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    Me too. Did you check them?

  56. Mertsj
    • one year ago
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    They both check.

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