Question

If `x=1/(3 - x),` find the value of `x + 1/x`.

Answer 1

Given, `x = 1/(3 - x),`

Let’s solve the equation first.

x(3 − x) = 1

3x − x² = 1

x² − 3x + 1 = 0

Now, dividing the whole equation by x:

`x^2/x - (3x)/x + 1/x = 0/x`

`x - 3+1/x = 0`

`x + 1/x = 0 + 3`

∴ `x + 1/x = 3`