Question

simplify the following rational expression.

\\\frac{x^2 + 6x + 5}{x^2 - 1}\\

\\\frac{x + ?}{x - \box}\\

Explanation:

Factor the numerator

Using the Factoring Trinomials knowledge point

$$ x^2 + 6x + 5 = (x + 5)(x + 1) $$

Factor the denominator

Using the Factoring Trinomials knowledge point

$$ x^2 - 1 = (x - 1)(x + 1) $$

Simplify the rational expression

Using the Simplifying Rational Expressions knowledge point

$$ \frac{x^2 + 6x + 5}{x^2 - 1} = \frac{(x + 5)(x + 1)}{(x - 1)(x + 1)} = \frac{x + 5}{x - 1} \quad (x eq -1, 1) $$

Answer:

Simplify the following rational expression.

$$ \frac{x^2 + 6x + 5}{x^2 - 1} $$

The simplified expression is \(\frac{x + [?]}{x - \Box}\), where the missing value in the numerator is <blank>5</blank>.