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Math Help - problems on solving rational equation

  1. #1
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    problems on solving rational equation

    so i've been given a question :
    5x / x-4 = 3x/2x + 7

    and i had to solve for x, or the root u can say. I've gotten to the step where i cross multiply and bring everything to one side. And i got
    7x^2 + 42 x, i'm not sure from here on how to solve for x or the roots.

    i also have another rational problem like this :
    x / x -2 = x^2-4x + 1/ x-3
    and i have gotten to the step of bring everything to one side :
    x^3 - 7x^2 + 12x -2 i'm not sure is this correct. but my teacher told me to solve with polynomial divison but i cannot find anything sets that polynomial to 0. so please help :S
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  2. #2
    Senior Member vincisonfire's Avatar
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     \frac{5x}{x-4} = \frac{3x}{2x + 7}
     5x \dot (2x+7) = 3x \cdot (x-4)
     10x^2 + 35x = 3x^2 - 12x
     7x^2 + 47x = 0
    Divide everything by x
     7x + 47 = 0
     x = -\frac{47}{7}
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  3. #3
    Senior Member vincisonfire's Avatar
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    \frac{x}{x -2} = \frac{x^2-4x + 1}{x-3}
    (x) \cdot (x-3) = (x^2-4x+1) \cdot (x-2)
     x^2 - 3x = x^3 - 4x^2+x-2x^2+8x-2
     0 = x^3 - 7x^2+12x-2
    This has no rational roots.
    Let  x = z - \frac{a}{3}
    Equation take form  0 = z^3 + pz + q
    That you can solve with a long messy method Cubic function - Wikipedia, the free encyclopedia
    Sorry there is not always a simple way.
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