Certainly! Let's solve the given expression step-by-step to understand how to arrive at the final result. The question is:
[tex]\[
\frac{[(-3)(-4) + (-1)(+2) - (1)(-2)]}{[(+2)(-2)]}
\][/tex]
### Step-by-Step Solution:
#### Step 1: Calculate the terms inside the numerator
First, we need to evaluate each term in the numerator separately.
1. [tex]\((-3)(-4)\)[/tex]
- Multiplying [tex]\(-3\)[/tex] and [tex]\(-4\)[/tex] gives us [tex]\(12\)[/tex].
- So, [tex]\((-3)(-4) = 12\)[/tex].
2. [tex]\((-1)(+2)\)[/tex]
- Multiplying [tex]\(-1\)[/tex] and [tex]\(+2\)[/tex] gives us [tex]\(-2\)[/tex].
- So, [tex]\((-1)(+2) = -2\)[/tex].
3. [tex]\((1)(-2)\)[/tex]
- Multiplying [tex]\(1\)[/tex] and [tex]\(-2\)[/tex] gives us [tex]\(-2\)[/tex].
- So, [tex]\((1)(-2) = -2\)[/tex].
The results of the computed terms are:
- [tex]\((-3)(-4) = 12\)[/tex]
- [tex]\((-1)(+2) = -2\)[/tex]
- [tex]\((1)(-2) = -2\)[/tex]
#### Step 2: Sum the results to get the numerator
Now let's combine these computed values:
[tex]\[
12 + (-2) - (-2)
\][/tex]
- Adding [tex]\(12\)[/tex] and [tex]\(-2\)[/tex] results in [tex]\(10\)[/tex].
- Subtracting [tex]\(-2\)[/tex] from [tex]\(10\)[/tex] is the same as adding [tex]\(2\)[/tex], giving us [tex]\(12\)[/tex].
Therefore, the numerator is [tex]\(12\)[/tex].
#### Step 3: Calculate the denominator
Next, we need to evaluate the denominator:
[tex]\[
(+2)(-2)
\][/tex]
- Multiplying [tex]\(+2\)[/tex] and [tex]\(-2\)[/tex] gives us [tex]\(-4\)[/tex].
Therefore, the denominator is [tex]\(-4\)[/tex].
#### Step 4: Divide the numerator by the denominator
Now we divide the numerator by the denominator:
[tex]\[
\frac{12}{-4}
\][/tex]
- Performing this division, we get [tex]\(-3\)[/tex].
### Final Answer:
So, the value of the given expression is:
[tex]\[
-3
\][/tex]
