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Perfect Square Trinomials

Factorise: x...

Question

Factorise:
$x^{2} + \frac{a^{2} + 1}{a} x + 1$ .

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Solution

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

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