Question

Factorise the following:

`x^2 + 1/x^2 - 2 - 3x + 3/x`

Answer 1

Given expression: `x^2 + 1/x^2 - 2 - 3x + 3/x`

Step-wise calculation:

1. Group terms to see if we can form perfect squares or known identities:

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

2. Notice that `x^2 + 1/x^2 - 2 = (x - 1/x)^2`

So the expression becomes:

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

3. Let `t = x - 1/x`

Hence, the expression simplifies to t² – 3t = t(t – 3).

4. Substitute back for t:

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