Question

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.

Answer 1

(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

Answer 2

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

Answer 3

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.

Answer 4

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)

Answer 5

Oops. Left off the last equals:

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