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wolfgirl

  • 4 years ago

(4)/(x-5)-(1)/(5) = (-5)/(5x-25)

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  1. wolfgirl
    • 4 years ago
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    |dw:1315244053369:dw|

  2. mfleisch5
    • 4 years ago
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    ok well ur gonna end up with this here hold on

  3. mfleisch5
    • 4 years ago
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    20-(5x-25)=-5

  4. mfleisch5
    • 4 years ago
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    so then (5x-25)=25

  5. mfleisch5
    • 4 years ago
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    then 5x=50 and then x=10 :)

  6. wolfgirl
    • 4 years ago
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    tht is very confusing to me, wht happened to the fractions?

  7. dhatraditya
    • 4 years ago
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    first step: subtract 1/5 from 4/x-5 and post what you get. you know how to subtract fractions I assume? take LCM and cross multiply to subtract the LHS expression

  8. dhatraditya
    • 4 years ago
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    |dw:1315244980380:dw|

  9. wolfgirl
    • 4 years ago
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    I got (-5)/(5(x-5))

  10. dhatraditya
    • 4 years ago
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    for the LHS or RHS?

  11. dhatraditya
    • 4 years ago
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    mfleisch5's answer is incorrect btw.

  12. wolfgirl
    • 4 years ago
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    oh ok

  13. dhatraditya
    • 4 years ago
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    I trust you can take it from there?

  14. wolfgirl
    • 4 years ago
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    I got (-5)/(5x-25)=(-5)/(5x-25)

  15. dhatraditya
    • 4 years ago
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    how did you get -5/(5x-25) on the left hand side of the equation? can you show me the steps?

  16. wolfgirl
    • 4 years ago
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    I multiplied the 5 and the x-5, then I thought the 4 was negative and added it with the 1

  17. dhatraditya
    • 4 years ago
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    no, draw and show me. I don't understand what you just said.

  18. dhatraditya
    • 4 years ago
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    first off all, 4 is not negative. secondly, that is not how you subtract fractions.

  19. wolfgirl
    • 4 years ago
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    ok what about (-1)/(5(x-25)) = (-1)/(5(x-25))

  20. dhatraditya
    • 4 years ago
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    |dw:1315245667613:dw|

  21. mfleisch5
    • 4 years ago
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    wolfgirl, all you have to do is multiply 5 and x-5. once u do that, you will have all common denominators, so you can cross them out. then you are left with what i gave you, and the answer is x=10

  22. dhatraditya
    • 4 years ago
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    |dw:1315245751739:dw|

  23. dhatraditya
    • 4 years ago
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    no mfleisch5, x=10 is not the correct answer.

  24. mfleisch5
    • 4 years ago
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    how is it not?

  25. wolfgirl
    • 4 years ago
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    I got 15

  26. dhatraditya
    • 4 years ago
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    \[\frac{4}{x-5} = \frac{4}{x-5} \times \frac{5}{5} = \frac{20}{5(x-5)}\]

  27. dhatraditya
    • 4 years ago
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    similarly, \[\frac{-1}{5} = \frac{-1}{5} \times \frac{x-5}{x-5} = \frac{-(x-5)}{5(x-5)}\]

  28. mfleisch5
    • 4 years ago
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    exactly. and then u multiply the other one by x-5

  29. dhatraditya
    • 4 years ago
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    so, \[\frac{4}{x-5} - \frac{1}{5} = \frac{20}{5(x-5)} - \frac{x-5}{5(x-5)} = \frac{20-(x-5)}{5(x-5)}\]

  30. mfleisch5
    • 4 years ago
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    no, because everything has 5(x-5) so u can take all of the denominators out

  31. dhatraditya
    • 4 years ago
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    so the left hand side is \[\frac{20-x+5}{5(x-5)} = \frac{25-x}{5(x-5)}\]

  32. dhatraditya
    • 4 years ago
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    now, the right hand side is \[\frac{-5}{5x-25} = \frac{-5}{5(x-5)}\]

  33. dhatraditya
    • 4 years ago
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    that means \[\frac{25-x}{5(x-5)} = \frac{-5}{5(x-5)}\]

  34. mfleisch5
    • 4 years ago
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    if that is true then that would mean there would be unlimited answers because no matter what u put for x it will work out. u are wrong hatra! its 10

  35. dhatraditya
    • 4 years ago
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    the denominators are the same on both sides of the equation. that means the numerators are equal too. so, \[25-x = -5\] solve for x.

  36. dhatraditya
    • 4 years ago
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    you get x = 30

  37. dhatraditya
    • 4 years ago
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    got it, wolfgirl? also, mfleisch5, you are still wrong. follow the steps I have shown.

  38. wolfgirl
    • 4 years ago
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    almost, there are a lot of numbers

  39. mfleisch5
    • 4 years ago
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    no. u are wrong. blah.

  40. dhatraditya
    • 4 years ago
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    ignore mfleisch5, ignore the pictures I drew, just follow the steps I have shown

  41. dhatraditya
    • 4 years ago
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    Let me know if you have any difficulties.

  42. wolfgirl
    • 4 years ago
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    alright I got it thanks :)

  43. dhatraditya
    • 4 years ago
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    also, mfleisch5, substitute 10 in the original equation and see if it is right. its a very easy test to see if your answer is correct or not.

  44. dhatraditya
    • 4 years ago
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    when you substitute x = 10 in \[\frac{4}{x-5}-\frac{1}{5} = \frac{-5}{5x-25} \] you get \[\frac{4}{10-5}-\frac{1}{5} = \frac{-5}{50-25} \rightarrow \frac{4}{5}-\frac{1}{5} = \frac{-5}{25}\] \[\frac{3}{5} = \frac{-1}{5}\]

  45. dhatraditya
    • 4 years ago
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    which is a contradiction. therefore x = 10 is not the correct answer.

  46. wolfgirl
    • 4 years ago
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    ok cool

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