Question

Factorization of $x^2+\frac{a^2-1}{a}x-1$ is

• A. $(x-\frac{1}{a})(x+a)$
• B. $(x-\frac{1}{a^2})(x+a)$
• C. $(x-\frac{1}{a^2})(x-a)$
• D. None of these

Answer 1

The correct option is A $(x-\frac{1}{a})(x+a)$

$x^2+\frac{a^2-1}{a}x-1=x^2+\left(\frac{a^2}{a}-\frac{1}{a}\right)x-1$
$=x^2+ax-\frac{x}{a}-1$
$=(x^2-\frac{x}{a})+(ax-1)$
$=x(x-\frac{1}{a})+a(x-\frac{1}{a})$
$=(x-\frac{1}{a})(x+a)$