What is expand ((n+1)^2)/(2n^2) ?

The solution to expand ((n+1)^2)/(2n^2) is 1/2+1/n+1/(2n^2)

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expand ((n+1)^2)/(2n^2)

expand

\frac{( n + 1 ) ^{2}}{2 n ^{2}}

\frac{1}{2} + \frac{1}{n} + \frac{1}{2 n ^{2}}

Solution steps

\frac{( n + 1 ) ^{2}}{2 n ^{2}}

(n + 1)^{2} = n^{2} + 2 n + 1

= \frac{n ^{2} + 2 n + 1}{2 n ^{2}}

Apply the fraction rule:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{n ^{2} + 2 n + 1}{2 n ^{2}} = \frac{n ^{2}}{2 n ^{2}} + \frac{2 n}{2 n ^{2}} + \frac{1}{2 n ^{2}}

= \frac{n ^{2}}{2 n ^{2}} + \frac{2 n}{2 n ^{2}} + \frac{1}{2 n ^{2}}

Cancel

\frac{n ^{2}}{2 n ^{2}} : \frac{1}{2}

= \frac{1}{2} + \frac{2 n}{2 n ^{2}} + \frac{1}{2 n ^{2}}

Cancel

\frac{2 n}{2 n ^{2}} : \frac{1}{n}

= \frac{1}{2} + \frac{1}{n} + \frac{1}{2 n ^{2}}

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What is expand ((n+1)^2)/(2n^2) ?
The solution to expand ((n+1)^2)/(2n^2) is 1/2+1/n+1/(2n^2)