To find the value of the expression [tex]\(\frac{a b + 2 c}{-b c}\)[/tex], we need to follow these steps:
1. Substitute the given values into the expression:
- [tex]\(a = -2\)[/tex]
- [tex]\(b = 3\)[/tex]
- [tex]\(c = -6\)[/tex]
2. Calculate [tex]\(a b + 2 c\)[/tex]:
- First, calculate [tex]\(a b\)[/tex]:
[tex]\[
a \cdot b = -2 \cdot 3 = -6
\][/tex]
- Next, calculate [tex]\(2 c\)[/tex]:
[tex]\[
2 \cdot c = 2 \cdot -6 = -12
\][/tex]
- Now, add the two results together:
[tex]\[
a b + 2 c = -6 + (-12) = -18
\][/tex]
3. Calculate the denominator, [tex]\(-b c\)[/tex]:
- First, calculate [tex]\(b c\)[/tex]:
[tex]\[
b \cdot c = 3 \cdot -6 = -18
\][/tex]
- Then apply the negative sign:
[tex]\[
-b c = -(-18) = 18
\][/tex]
4. Evaluate the entire expression:
[tex]\[
\frac{a b + 2 c}{-b c} = \frac{-18}{18} = -1.0
\][/tex]
Thus, the value of the expression is [tex]\(-1.0\)[/tex].
