Question

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

Answer 1

This equation has no real solutions

Explanation:

`1/x+1/2x=1/6`

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

`6+3x^2=x`
`3x^2-x+6=0`

Now we look for the solutions of a quadratic equation:

`Delta=(-1)^2-4*3*6=1-72=-71`
`Delta<0` so this equation has no real solutions.

So the base equation also has no real solutions.

Answer 2

Is there a formatting problem in the question?

Should it have been:

How do you solve `1/x+1/(2x)=1/6` ?

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

Explanation:

Assuming the problem is:

How do you solve `1/x+1/(2x)=1/6` ?

Multiply both sides by `6x` to get:

`6+3 = x`

So `x=9`