Question

for which rational expression is -5 an excluded value of x?
$\frac{x - 5}{6}$
$\frac{x + 5}{6}$
$\frac{6}{x - 5}$
$\frac{6}{x + 5}$

Explanation:

Step1: Recall excluded value rule

Excluded values make denominator = 0.

Step2: Test each option's denominator

• Option 1: Denominator $6

eq 0$ for any $x$.

• Option 2: Denominator $6

eq 0$ for any $x$.

• Option 3: Set $x-5=0$, solve $x=5$.
• Option 4: Set $x+5=0$, solve $x=-5$.

Answer:

$\boldsymbol{\frac{6}{x+5}}$