To evaluate the given expression for [tex]\(k = -2\)[/tex] and [tex]\(m = -2\)[/tex], we need to follow several steps to simplify it and find the final result. The expression to evaluate is:
[tex]\[
\frac{k^2 m - k}{m}
\][/tex]
First, substitute the given values of [tex]\(k\)[/tex] and [tex]\(m\)[/tex] into the expression:
[tex]\[
k = -2 \quad \text{and} \quad m = -2
\][/tex]
Next, substitute [tex]\( k \)[/tex] and [tex]\( m \)[/tex] into the expression:
[tex]\[
\frac{(-2)^2 \cdot (-2) - (-2)}{-2}
\][/tex]
Let's break this down step by step:
1. Compute [tex]\( (-2)^2 \)[/tex]:
[tex]\[
(-2)^2 = 4
\][/tex]
2. Multiply this result by [tex]\( m = -2 \)[/tex]:
[tex]\[
4 \cdot (-2) = -8
\][/tex]
3. Subtract [tex]\( k = -2 \)[/tex]:
[tex]\[
-8 - (-2) = -8 + 2 = -6
\][/tex]
Now, place this result in the numerator and divide by [tex]\( m = -2 \)[/tex]:
[tex]\[
\frac{-6}{-2}
\][/tex]
4. Simplify the fraction:
[tex]\[
\frac{-6}{-2} = 3
\][/tex]
Thus, the simplified value of the expression is:
[tex]\[
3
\][/tex]
So, the final answer is:
[tex]\[
\boxed{3}
\][/tex]
