Question

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

Answer 1

`-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)`