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Math Help - Fractions with unknow numbers

  1. #1
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    Fractions with unknow numbers

    The numerator of a fraction is 1 less than the denominator. When both numerator and denominator are increased by 2, the fraction is increased by 1/12. Find the original fraction. (One should try to solve it by completing the square)

    This is my attempt:
    x+1/x+2-(x-1)/x=1/12
    After that I multiplied everything with (x+2) 12x and cancelled out the numbers. I am not sure if the first equation is correct.
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  2. #2
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    Quote Originally Posted by Anna55 View Post
    The numerator of a fraction is 1 less than the denominator. When both numerator and denominator are increased by 2, the fraction is increased by 1/12. Find the original fraction. (One should try to solve it by completing the square)

    This is my attempt:
    x+1/x+2-(x-1)/x=1/12
    After that I multiplied everything with (x+2) 12x and cancelled out the numbers. I am not sure if the first equation is correct.
    your set-up is correct ...

    \dfrac{x+1}{x+2} - \dfrac{x-1}{x} = \dfrac{1}{12}

    ... and your subsequent method will work fine.
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  3. #3
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    I tried to solve the equation, however I got the wrong answer. Can you please show me how to solve it? Thank you!
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  4. #4
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    When you expand and simplify 12x(x+1)-12(x+2)(x-1)=x(x+2)
    what did you get?
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  5. #5
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    I got this:
    (x+1)12x-(x-1)12(x+2)=1x (x+2)
    12x^2+12x-(x-1)12x+24=x^2+2x
    Did I make a mistake?
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  6. #6
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    Quote Originally Posted by Anna55 View Post
    I got this:
    (x+1)12x-(x-1)12(x+2)=1x (x+2)
    12x^2+12x-(x-1)12x+24=x^2+2x
    Did I make a mistake?
    The part in red should be -12x^2-12x+24
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  7. #7
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    You haven't multiplied the -(x-1) by 24 as well as the 12x. The 12x+24 should be in brackets i.e -(x-1)(12x+24)...
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  8. #8
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    You should end up with x^2 +12x-24=0
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  9. #9
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    Quote Originally Posted by orlacoon View Post
    You should end up with x^2 +12x-24=0
    incorrect ... x^2 + 2x - 24 = 0
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  10. #10
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    Sorry-Typo

    Sorry- that was a typo. Meant to say x^2+2x-24=0. The equation x^2+12x-24=0 is what you would get using the asker's workings out!
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