Question

Factorise the following:

`x^2 - (a/b + b/a)x + 1`

Answer 1

Given expression: `x^2 - (a/b + b/a)x + 1`

Step-wise calculation:

1. Rewrite the middle term by considering the sum inside:

`x^2 - a/bx - b/a x + 1`

2. Find a common denominator to combine the fractions; but here, focus on grouping terms to factor:

`x^2 - a/b x - b/a x + 1`

= `x^2 - a/b x - b/a x + (ab)/(ab)`

3. Group terms in a way to factor common expressions:

`x(x - a/b) - 1/(a//b) (x - a/b)`

Note: `1/(a//b) = b/a`.

4. Factor out the common binomial factor:

`(x - a/b)(x - b/a)`