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Math Help - Solution sets and simplest forms

  1. #1
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    Solution sets and simplest forms

    i was wondering if anyone could help me out with these two problems?!

    expressed in simplest form: 5x+3/x - x-1/2x is??

    and the solution set of? 3x+2/x=4x-2/3x+1/3




    Thanks for any help!
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  2. #2
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    1) expressed in simplest form: 5x+3/x - x-1/2x is??

    So first I'm interpreting this as 5x + 3/x - x - 1/(2x). that is the problem I am solving.

    Step 1: bring to a common denominator

    5x(2x/2x) + 3/x(2x/2x) - x(2x/2x) - (1/(2x))(2x/2x)

    simplified: 10(x^2)/(2x) + 6/(2x) - 2(x^2)/(2x) - 1/(2x)

    Step 2: add/subtract

    (10(x^2) + 6 - 2(x^2) - 1)/(2/x)

    Simplify

    (8(x^2) + 5)/(2x)


    2) and the solution set of? 3x+2/x=4x-2/3x+1/3

    Interpretation: 3x + 2/x = 4x - (2/3)x + 1/3 is it (2/3)x or 2/(3x)?

    Step 1: Multiply through by 3x to get rid of denominators

    3x(3x + 2/x) = 3x(4x - (2/3)x + 1/3)

    simplify

    9(x^2) + 6 = 12(x^2) - 2(x^2) + x

    simplify more

    9(x^2) + 6 = 10(x^2) + x

    Step 2: subtract left side to get all values on right side

    0 = x^2 + x - 6

    Step 3: Factor

    0 = (x + 3)(x - 2)

    so x = -3,2

    if it's 2/(3x) then it's the same procedure but the quadratic won't factor nicely, so you use the quadratic formula

    hopefully that wasn't too confusing
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