To find an expression equivalent to [tex]\(\frac{2}{7 k}(k-7)\)[/tex], let's simplify it step-by-step. Assume [tex]\(k \neq 0\)[/tex].
The expression is:
[tex]\[
\frac{2}{7 k}(k-7)
\][/tex]
1. Distribute [tex]\(\frac{2}{7 k}\)[/tex] over the terms inside the parenthesis:
[tex]\[
= \frac{2}{7 k} \cdot k - \frac{2}{7 k} \cdot 7
\][/tex]
2. Simplify each term separately:
[tex]\[
= \frac{2k}{7 k} - \frac{2 \cdot 7}{7 k}
\][/tex]
3. Simplify the fractions:
[tex]\[
= \frac{2}{7} - \frac{2 \cdot 7}{7 k}
\][/tex]
Since [tex]\(\frac{2 \cdot 7}{7 k}\)[/tex] can be simplified further:
[tex]\[
= \frac{2}{7} - \frac{2}{k}
\][/tex]
Thus, the simplified form of the original expression is:
[tex]\[
\frac{2}{7} - \frac{2}{k}
\][/tex]
Therefore, the expression [tex]\(\frac{2}{7 k}(k-7)\)[/tex] is equivalent to:
[tex]\[
\frac{2}{7} - \frac{2}{k}
\][/tex]
From the given choices, the correct option is:
[tex]\[
\frac{2}{7} - \frac{2}{k}
\][/tex]
