select the correct answer.\nthe difference of half a number and its reciprocal is represented by this…

select the correct answer.\nthe difference of half a number and its reciprocal is represented by this expression.\n\\( \\frac { n } { 2 } - \\frac { 1 } { n } \\)\nwhich expression also represents the difference?\na. \\( \\frac { n ^ { 2 } - 2 } { 2 n } \\)\nb. \\( \\frac { n - 1 } { 2 - n } \\)\nc. \\( \\frac { n ^ { 2 } - 1 } { 2 - n } \\)\nd. \\( \\frac { n ^ { 2 } } { 2 n } \\)

select the correct answer.\nthe difference of half a number and its reciprocal is represented by this expression.\n\\( \\frac { n } { 2 } - \\frac { 1 } { n } \\)\nwhich expression also represents the difference?\na. \\( \\frac { n ^ { 2 } - 2 } { 2 n } \\)\nb. \\( \\frac { n - 1 } { 2 - n } \\)\nc. \\( \\frac { n ^ { 2 } - 1 } { 2 - n } \\)\nd. \\( \\frac { n ^ { 2 } } { 2 n } \\)

Answer

Explanation:

Step1: Find a common denominator

To combine the fractions (\frac{n}{2}) and (\frac{1}{n}), the common denominator is (2n). Rewrite each fraction with the common denominator: (\frac{n}{2}=\frac{n\times n}{2\times n}=\frac{n^{2}}{2n}) (\frac{1}{n}=\frac{1\times 2}{n\times 2}=\frac{2}{2n})

Step2: Subtract the fractions

Now subtract the two fractions: (\frac{n}{2}-\frac{1}{n}=\frac{n^{2}}{2n}-\frac{2}{2n}=\frac{n^{2} - 2}{2n})

Answer:

A. (\frac{n^{2}-2}{2n})