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Which expression is equivalent to [tex]\frac{2}{7k}(k-7)[/tex]? Assume [tex]k \neq 0[/tex].

A. [tex]\frac{2}{7-k}[/tex]

B. [tex]\frac{2}{7}-\frac{2}{k}[/tex]

C. [tex]\frac{2k}{7}-7[/tex]

D. [tex]\frac{2k}{7k}-2k[/tex]

Sagot :

GinnyAnswer
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]
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