What is expand (4(n+1)(2n+1))/(3n^2) ?

The solution to expand (4(n+1)(2n+1))/(3n^2) is 8/3+4/n+4/(3n^2)

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expand (4(n+1)(2n+1))/(3n^2)

expand

\frac{4 ( n + 1 ) ( 2 n + 1 )}{3 n ^{2}}

\frac{8}{3} + \frac{4}{n} + \frac{4}{3 n ^{2}}

Solution steps

\frac{4 ( n + 1 ) ( 2 n + 1 )}{3 n ^{2}}

Expand

4 (n + 1) (2 n + 1) : 8 n^{2} + 12 n + 4

= \frac{8 n ^{2} + 12 n + 4}{3 n ^{2}}

Apply the fraction rule:

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

\frac{8 n ^{2} + 12 n + 4}{3 n ^{2}} = \frac{8 n ^{2}}{3 n ^{2}} + \frac{12 n}{3 n ^{2}} + \frac{4}{3 n ^{2}}

= \frac{8 n ^{2}}{3 n ^{2}} + \frac{12 n}{3 n ^{2}} + \frac{4}{3 n ^{2}}

Cancel

\frac{8 n ^{2}}{3 n ^{2}} : \frac{8}{3}

= \frac{8}{3} + \frac{12 n}{3 n ^{2}} + \frac{4}{3 n ^{2}}

Cancel

\frac{12 n}{3 n ^{2}} : \frac{4}{n}

= \frac{8}{3} + \frac{4}{n} + \frac{4}{3 n ^{2}}

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What is expand (4(n+1)(2n+1))/(3n^2) ?
The solution to expand (4(n+1)(2n+1))/(3n^2) is 8/3+4/n+4/(3n^2)