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

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

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

expand

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

2 + \frac{3}{n} + \frac{1}{n ^{2}}

Solution steps

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

Expand

(n + 1) (2 n + 1) : 2 n^{2} + 3 n + 1

= \frac{2 n ^{2} + 3 n + 1}{n ^{2}}

Apply the fraction rule:

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

\frac{2 n ^{2} + 3 n + 1}{n ^{2}} = \frac{2 n ^{2}}{n ^{2}} + \frac{3 n}{n ^{2}} + \frac{1}{n ^{2}}

= \frac{2 n ^{2}}{n ^{2}} + \frac{3 n}{n ^{2}} + \frac{1}{n ^{2}}

Cancel

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

= 2 + \frac{3 n}{n ^{2}} + \frac{1}{n ^{2}}

Cancel

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

= 2 + \frac{3}{n} + \frac{1}{n ^{2}}

\frac{s}{( s ^{2} - 4 ) ^{2}}

(3 b - \frac{4}{b})^{7}

(1 + \frac{3 i}{n})^{3}

(x^{3} - \frac{1}{2 x})^{12}

(3 - x 3)^{2}

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