When [tex]x=-6,[/tex] the value of the expression becomes undefined so it is the non-permissible replacement for the expression.
Step-by-step explanation:
Step 1:
To determine the non-permissible replacement we substitute x with the values of 6, 3, -3, and -6.
When [tex]x=6, \frac{3-x}{6+x} = \frac{3-6}{6+6}=-\frac{3}{12} = -\frac{1}{4}[/tex],
When [tex]x=3, \frac{3-x}{6+x} = \frac{3-3}{6+3}=\frac{0}{9}=0[/tex],
When [tex]x=-3, \frac{3-x}{6+x} = \frac{3-(-3)}{6+(-3)}=\frac{6}{3} =2,[/tex],
When [tex]x=-6, \frac{3-x}{6+x} = \frac{3-(-6)}{6+(-6)}=\frac{9}{0}[/tex], any value, when divided by a zero, becomes undefined.
Step 2:
The values of options a, b, and c all have numerical values.
When [tex]x=-6,[/tex] the value of the expression becomes undefined so it is the non-permissible replacement for the expression.
