Question

due wednesday by 11:59pm points 100 submitting an external tool current objective simplify rational expressions switch question simplify the following rational expression. $\frac{x^{2}-1}{x^{2}+5x - 6}$ give your answer as a reduced rational expression. sorry, thats incorrect. try again? previous

Explanation:

Step1: Factor the numerator

Use the difference - of - squares formula \(a^{2}-b^{2}=(a + b)(a - b)\). Here, \(x^{2}-1=(x + 1)(x - 1)\).

Step2: Factor the denominator

We need to find two numbers that multiply to \(-6\) and add up to \(5\). The numbers are \(6\) and \(-1\). So, \(x^{2}+5x - 6=(x + 6)(x-1)\).

Step3: Simplify the rational expression

Cancel out the common factor \((x - 1)\) in the numerator and denominator. \(\frac{(x + 1)(x - 1)}{(x + 6)(x - 1)}=\frac{x + 1}{x+6}\), where \(x
eq1\) (to avoid division by zero in the original expression).

Answer:

\(\frac{x + 1}{x + 6}\)