Question

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\\) a. \\(\frac{n^2 - 2}{2n}\\)
\\(\bigcirc\\) b. \\(\frac{n - 1}{2 - n}\\)
\\(\bigcirc\\) c. \\(\frac{n^2 - 1}{2 - n}\\)
\\(\bigcirc\\) d. \\(\frac{n^2}{2n}\\)

Explanation:

Step1: Find a common denominator for the two terms

The two terms are $\frac{n}{2}$ and $\frac{1}{n}$. The common denominator of 2 and $n$ is $2n$.

Step2: Rewrite each term with the common denominator

For $\frac{n}{2}$, multiply numerator and denominator by $n$: $\frac{n\times n}{2\times n}=\frac{n^{2}}{2n}$.
For $\frac{1}{n}$, multiply numerator and denominator by 2: $\frac{1\times 2}{n\times 2}=\frac{2}{2n}$.

Step3: Subtract the two rewritten terms

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

Answer:

A. $\frac{n^{2}-2}{2n}$