Let's solve the given expression step-by-step.
Given expression:
[tex]\[
\frac{-2(5+3) - 9 \div 3 + 5}{-3 \times -5 + 2 \times 4}
\][/tex]
### Step 1: Evaluate the numerator
First, we simplify the numerator:
[tex]\[
-2(5+3) - 9 \div 3 + 5
\][/tex]
#### Step 1.1: Resolve the parentheses
[tex]\[
-2(8) - 9 \div 3 + 5
\][/tex]
#### Step 1.2: Perform the multiplication and division
[tex]\[
-16 - 3 + 5
\][/tex]
#### Step 1.3: Combine the terms
[tex]\[
-16 + 5 - 3 = -14
\][/tex]
So, the numerator is [tex]\(-14\)[/tex].
### Step 2: Evaluate the denominator
Now, we simplify the denominator:
[tex]\[
-3 \times -5 + 2 \times 4
\][/tex]
#### Step 2.1: Perform the multiplications
[tex]\[
15 + 8
\][/tex]
#### Step 2.2: Add the results
[tex]\[
23
\][/tex]
So, the denominator is [tex]\(23\)[/tex].
### Step 3: Perform the division
Finally, we divide the numerator by the denominator:
[tex]\[
\frac{-14}{23}
\][/tex]
This simplifies to approximately [tex]\(-0.6087\)[/tex].
### Final Answer
The evaluated result of the given expression is:
[tex]\[
\frac{-2(5+3)-9 \div 3+5}{-3 \times -5+2 \times 4} = -0.6087
\][/tex]
