How do you solve #1/2x + 3/(x+7) = -1/x #?

1 Answer
Dec 16, 2017

Answer:

#-6.061205...#

Explanation:

#x/2+3/(x+7)=-1/x#
You have to get a common denominator, in this case, it would be #2(x)(x+7)#. Therefore, you would multiply all the terms by a form of 1 to get #(x)(x+7)(x/2)+(2)(x)(3/(x+7))=(2)(x+7)(-1/x)#.
This gives you #(x^3+7x^2)/(2x^2+14x)+(6x)/(2x^2+14x)=(-2x-14)/(2x^2+14x)#.
Since the denominators are now all the same, they can be ignored: #x^3+7x^2+6x=-2x-14#.
When you combine like terms and put everything on the same side, you get #x^3+7x^2+8x+14#.
From here, since it doesn't factor easily, I would recommend you solve it graphically if you are allowed to. graph{x^3+7x^2+8x+14 [-81.04, 81.1, -40.6, 40.46]}
#(-6.061205...,0)#