Question

select the correct answer.

the difference of half a number and its reciprocal is represented by this expression.

\\\frac{n}{2} - \frac{1}{n}\\

which expression also represents the difference?

\\(\bigcirc\\) \\(\frac{n^2 - 2}{2n}\\)

\\(\bigcirc\\) \\(\frac{n^2}{2n}\\)

\\(\bigcirc\\) \\(\frac{n^2 - 1}{2 - n}\\)

\\(\bigcirc\\) \\(\frac{n - 1}{2 - n}\\)

Explanation:

Find the least common denominator

$$ \text{LCD}(2, n) = 2n $$

Rewrite each term with the common denominator

$$ \frac{n}{2} - \frac{1}{n} = \frac{n \cdot n}{2 \cdot n} - \frac{1 \cdot 2}{n \cdot 2} $$

Subtract the numerators

$$ \frac{n^2}{2n} - \frac{2}{2n} = \frac{n^2 - 2}{2n} $$

Answer:

• (A) \(\frac{n^2 - 2}{2n}\) (Correct answer)
• (B) \(\frac{n^2}{2n}\)
• (C) \(\frac{n^2 - 1}{2 - n}\)
• (D) \(\frac{n - 1}{2 - n}\)