Question

identify the excluded value(s) of the rational expression.
\frac{x^2+2x-3}{x^2+5x+6}
-3
-2
1
2
3

Explanation:

⚡ Using what you learned: Identifying Restrictions and Asymptotes

Step 1: Identify the condition for excluded values

Excluded values of a rational expression are the values of \( x \) that make the denominator equal to zero, as division by zero is undefined.

Set the denominator equal to zero:

$$ x^2 + 5x + 6 = 0 $$

Step 2: Factor the quadratic equation

Find two numbers that multiply to \( 6 \) and add up to \( 5 \). These numbers are \( 2 \) and \( 3 \).

$$ (x + 2)(x + 3) = 0 $$

Step 3: Solve for \( x \)

Set each factor to zero:

$$ x + 2 = 0 \implies x = -2 $$

$$ x + 3 = 0 \implies x = -3 $$

The excluded values are \( -3 \) and \( -2 \).

Answer:

• \(-3\)
• \(-2\)