Question

How do you solve `x/3 - 2/3 = 1/x`?

Answer 1

`x/3 - 2/3 = 1/x`

`(x-2)/3 = 1/x`

cross multiplying:
`x(x-2) = 1.3`
`x^2 - 2x = 3`
`x^2 - 2x - 3 = 0`

Factorising the term to find solutions:

Splitting the middle term:
`x^2 - 3x + x - 3 = 0`
`x(x- 3) + 1(x - 3) = 0`

the solutions are `color(blue)(x = -1 , x=3`