Question

Factorise:

$x^2+\frac{a^2+1}{a}x+1$

Answer 1

$x^2+\frac{a^2+1}{a}x+1\Rightarrow x^2+(a+\frac{1}{a})x+1\Rightarrow x^2+ax+\frac{x}{a}+1\Rightarrow x(x+a)+\frac{1}{a}(x+a)\Rightarrow (x+a)(x+\frac{1}{a})$