simplify the expression completely if possible. \n\\( \\frac { x ^ { 2 } - 1 } { x ^ { 2 } + 5 x - 6 } \\)

Answer:

$\frac{x - 1}{x - 1}$

Explanation:

Step1: Factor numerator and denominator

Numerator: $x^{2}-1=(x + 1)(x - 1)$ (using $a^{2}-b^{2}=(a + b)(a - b)$). Denominator: $x^{2}+5x - 6=(x + 6)(x - 1)$ (factoring quadratic $ax^{2}+bx + c$). So the expression becomes $\frac{(x + 1)(x - 1)}{(x + 6)(x - 1)}$.

Step2: Cancel common factors

Cancel out the common factor $(x - 1)$ (assuming $x\neq1$). We get $\frac{x + 1}{x + 6}$.