Question

identifying excluded values
identify the excluded value(s) of the rational expression. choose two correct answers.
\\(\frac{x^2 + 2x - 3}{x^2 + 5x + 6}\\)
options: -2, 1, 2, 3, -3

Explanation:

Step1: Recall excluded values rule

For a rational expression \(\frac{f(x)}{g(x)}\), excluded values are when \(g(x) = 0\) (since division by zero is undefined). So we need to solve \(x^{2}+5x + 6=0\).

Step2: Factor the denominator

Factor \(x^{2}+5x + 6\). We look for two numbers that multiply to \(6\) and add to \(5\). Those numbers are \(2\) and \(3\). So \(x^{2}+5x + 6=(x + 2)(x+3)\).

Step3: Solve for x

Set each factor equal to zero:

• \(x + 2=0\) gives \(x=-2\).
• \(x + 3=0\) gives \(x=-3\).

Answer:

-2, -3 (corresponding to the options: the box with -2, the box with -3)