Question

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

Answer 1

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

cross multiplying

`x(x-2) = 3`
`x^2 - 2x = 3`
`x^2 - 2x - 3=0`

splitting the middle term and factorising the expression:
`x^2 - 3x +1x- 3 = 0`
`x(x-3) + 1(x-3) = 0`
`(x+1)(x-3) =0`

the solutions for the equation are `color(red)(x=-1 and x=3`