Question

How do you solve `\frac { 1} { x } + \frac { 1} { 3} = \frac { 8} { 3} x`?

Answer 1

`x=(1+-sqrt(97))/16`

Explanation:

First you would subtract `1/3` from both sides
this would give you `1/x=(8x-1)/3`
then you would cross multiply to get `3=8x^2-x`
subtract 3 to get `8x^2-x-3`
use the quadratic formula:
`(-(-1)+-sqrt((-1)^2-4(8)(-3)))/16`
that simplifies to `(1+-sqrt(97))/16`