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

Dec 16, 2017

$- 6.061205 \ldots$

#### Explanation:

$\frac{x}{2} + \frac{3}{x + 7} = - \frac{1}{x}$
You have to get a common denominator, in this case, it would be $2 \left(x\right) \left(x + 7\right)$. Therefore, you would multiply all the terms by a form of 1 to get $\left(x\right) \left(x + 7\right) \left(\frac{x}{2}\right) + \left(2\right) \left(x\right) \left(\frac{3}{x + 7}\right) = \left(2\right) \left(x + 7\right) \left(- \frac{1}{x}\right)$.
This gives you $\frac{{x}^{3} + 7 {x}^{2}}{2 {x}^{2} + 14 x} + \frac{6 x}{2 {x}^{2} + 14 x} = \frac{- 2 x - 14}{2 {x}^{2} + 14 x}$.
Since the denominators are now all the same, they can be ignored: ${x}^{3} + 7 {x}^{2} + 6 x = - 2 x - 14$.
When you combine like terms and put everything on the same side, you get ${x}^{3} + 7 {x}^{2} + 8 x + 14$.
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]}
$\left(- 6.061205 \ldots , 0\right)$