Certainly! Let's break the problem down step-by-step. We need to evaluate the expression:
[tex]\[
\frac{-8 + (-5) \times (-8) - (-6)}{-3 + (-8) + 2 \times 4}
\][/tex]
### Step 1: Evaluate the numerator
The numerator of the fraction is:
[tex]\[
-8 + (-5) \times (-8) - (-6)
\][/tex]
First, we need to handle the multiplication:
[tex]\[
(-5) \times (-8) = 40
\][/tex]
Next, we substitute this result back into the numerator:
[tex]\[
-8 + 40 - (-6)
\][/tex]
Now, note that subtracting a negative number is the same as adding the positive equivalent:
[tex]\[
-8 + 40 + 6
\][/tex]
Let's add these values in sequence:
[tex]\[
-8 + 40 = 32
\][/tex]
[tex]\[
32 + 6 = 38
\][/tex]
So, the numerator is:
[tex]\[
38
\][/tex]
### Step 2: Evaluate the denominator
The denominator of the fraction is:
[tex]\[
-3 + (-8) + 2 \times 4
\][/tex]
First, we need to handle the multiplication:
[tex]\[
2 \times 4 = 8
\][/tex]
Next, we substitute this result back into the denominator:
[tex]\[
-3 + (-8) + 8
\][/tex]
Now, let's add these values in sequence:
[tex]\[
-3 + (-8) = -11
\][/tex]
[tex]\[
-11 + 8 = -3
\][/tex]
So, the denominator is:
[tex]\[
-3
\][/tex]
### Step 3: Combine the numerator and the denominator
Now we have the numerator and the denominator evaluated, so we can substitute them into the fraction:
[tex]\[
\frac{38}{-3}
\][/tex]
Simplify this to obtain the result:
[tex]\[
38 \div -3 = -\frac{38}{3}
\][/tex]
This fraction can be represented as a decimal:
[tex]\[
-\frac{38}{3} \approx -12.666666666666666
\][/tex]
So, the final result is:
[tex]\[
\boxed{-12.666666666666666}
\][/tex]
Thus, evaluating the given expression yields [tex]\(\frac{38}{-3}\)[/tex] or approximately [tex]\(-12.67\)[/tex].
