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## Sagot :

Let's set the denominator [tex]\(-6x - 3\)[/tex] equal to zero and solve for [tex]\(x\)[/tex]:

[tex]\[ -6x - 3 = 0 \][/tex]

First, add 3 to both sides of the equation:

[tex]\[ -6x - 3 + 3 = 0 + 3 \implies -6x = 3 \][/tex]

Next, divide both sides by -6:

[tex]\[ x = \frac{3}{-6} \][/tex]

Simplify the fraction:

[tex]\[ x = -\frac{1}{2} \][/tex]

Therefore, the value that makes the denominator zero and thus makes the expression undefined is:

[tex]\[ x = -\frac{1}{2} \][/tex]

So, the excluded value for the expression [tex]\(\frac{8}{-6x - 3}\)[/tex] is:

[tex]\[ x = -\frac{1}{2} \][/tex]