Pre Calc still confused

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Solve: (x+5/x)+(6/x-4)=(-7/x^2-4x)

I multiplied the entire function by x and x-4 and after doing that I got down to the quadratic equation
x^2+7x-13=0

I did the quadratic and got

x=1.525 and -8.525

I feel like I made a mistake because when I plug in both of those answers for x separately, it never works out. Not sure if I made an error in calculating or in plugging in, or if there is no solution.

Thanks.

  • Pre Calc still confused -

    (x+5)(x-4)+ 6x=-7
    x^2+x-20+6x=-7
    x^2+7x-13=0

    x= (-7 +-sqrt (49+52))/2=(-7+-10.04)/2
    x=-17/2, 3/2 your answers

  • Pre Calc one more thing -

    When I plug them in they don't work. am I plugging them in wrong or is it no solution?

  • Pre Calc still confused -

    Are the brackets right?

    I've tried

    (x+5/x)+(6/x-4)=(-7/x^2-4x),

    and

    (x+5)/x + 6/(x-4)=-7/(x^2-4x)
    and a couple of other permutations without achieving enlightenment.

  • Pre Calc still confused -

    OK. If it's

    (x+5)/x + 6/(x-4)=-7/(x^2-4x)

    then I agree with bobpursley's answer

    but the numerical answers aren't exactly -17/2 and 3/2; they're
    (-7+-sqrt(101))/2. If you plug 3/2 in, it'll be close but not zero.


    6.5/1.5 + 6/(1.5-4)+7/(1.5^2-4*1.5)

  • Pre Calc still confused -

    Oops. Left off the last equals:

    6.5/1.5 + 6/(1.5-4)+7/(1.5^2-4*1.5) = 0.066666...

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