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Math Help - Find in terms of C

  1. #1
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    Find in terms of C

    Having trouble with making the common denominator work. please help.

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    Find x in terms of c, given that ( 2 / 3x - 2c ) + (3 / 2x - 3c) = 7 / 2c
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  2. #2
    MHF Contributor Amer's Avatar
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    just a question

    (\frac{2}{3x}-2c)+(\frac{3}{2x}-3c)=\frac{7}{2c}

    or

    (\frac{2}{3x-2c})+(\frac{3}{2x-3c})=\frac{7}{2c}
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    this is the exact question, sorry about the inital setout.
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  4. #4
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    Quote Originally Posted by Joel View Post



    this is the exact question, sorry about the inital setout.
    Then don't worry about "common denominator" or adding fractions: multiply the entire equation by (3x-2c)(2x- 3c)(2c) (which is, actually, the "common denominator.)

    Multiplying the first term by that, \frac{2}{3x-2c}(3x-2c)(2x-3c)(2c), the "3x- 2c" terms cancel leaving 2(2x-3c)(2c)= 4c(2x-3c)= 8cx- 12c^2. Multiplying the second term by that, \frac{3}{2x-3c}(3x-2c)(2x-3c)(2c), the "2x-3c" terms cancel leaving 3(2c)(2x-3c)= 6c(2x-3c)= 12cx- 18c^2. Finally, multiplying the right hand side of the equation by that, \frac{7}{2c}(3x-2c)(2x-3c)(2c), the "2c" terms cancel leaving 7(3x-2c)(2x-3c)= 7(6x^2-10cx+ 6c^2)= 42x^2- 70cx+ 42c^2.

    Putting those together, multiplying the entire equation by (3x-2c)(2x-3c)(2c) changes the equation to 8cx- 12c^2+ 12cx- 18c^2= 42x^2- 70cx+ 42c^2 or 20cx- 30c^2= 42x^2- 70cx+ 42c^2, 42x^2- 90cx+ 72c^2= 0. Dividing through by 2, 21x^2- 45cx+ 36c^2= 0.

    That appears, to me, to not have any real roots.
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