## Elementary Algebra

$\frac{(x+1)}{3x}$
To factor the numerator, we use the rule $a^{2}-b^{2}=(a+b)(a-b)$. Then, we factor the expression in the denominator in order to cancel out common factors in the numerator and the denominator: $\frac{x^{2}-1}{3x^{2}-3x}$ =$\frac{x^{2}-1^{2}}{3x(x-1)}$ =$\frac{(x+1)(x-1)}{3x(x-1)}$ =$\frac{(x+1)}{3x}$