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Thread: please help algebra question. solve for x

  1. #1
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    please help algebra question. solve for x

    (x-8)/(x^2-x-42)= 1+8/(x-7)

    solve for x.

    i got 7.75 but it is saying its not right any help?
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  2. #2
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    Quote Originally Posted by huh1 View Post
    (x-8)/(x^2-x-42)= 1+8/(x-7)

    solve for x.

    i got 7.75 but it is saying its not right any help?
    $\displaystyle \frac{x-8}{(x-7)(x+6)} = \frac{x-7}{x-7} + \frac{8}{x-7}$

    $\displaystyle \frac{x-8}{(x-7)(x+6)} = \frac{x+1}{x-7}$

    $\displaystyle \frac{x-8}{(x-7)(x+6)} = \frac{(x+1)(x+6)}{(x-7)(x+6)}$

    numerators form the equation ...

    $\displaystyle x-8 = (x+1)(x+6)$

    $\displaystyle x-8 = x^2 + 7x + 6$

    $\displaystyle 0 = x^2 + 6x + 14$

    this quadratic has no real solution
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  3. #3
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    Thank you so much! I figured it was no real solution, but I couldn't actually prove it. haha. Thanks again.
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