# How do you solve 1/x + 1/2x = 1/6 ?

Jun 21, 2015

This equation has no real solutions

#### Explanation:

$\frac{1}{x} + \frac{1}{2} x = \frac{1}{6}$

First we multiply both sides by $6 x$ to get rid of the fractions and the unknown in the denominator:

$6 + 3 {x}^{2} = x$
$3 {x}^{2} - x + 6 = 0$

Now we look for the solutions of a quadratic equation:

$\Delta = {\left(- 1\right)}^{2} - 4 \cdot 3 \cdot 6 = 1 - 72 = - 71$
$\Delta < 0$ so this equation has no real solutions.

So the base equation also has no real solutions.

Jun 21, 2015

Is there a formatting problem in the question?

Should it have been:

How do you solve $\frac{1}{x} + \frac{1}{2 x} = \frac{1}{6}$ ?

If so, $x = 9$ is the solution.

#### Explanation:

Assuming the problem is:

How do you solve $\frac{1}{x} + \frac{1}{2 x} = \frac{1}{6}$ ?

Multiply both sides by $6 x$ to get:

$6 + 3 = x$

So $x = 9$