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

The solution to expand (3(n+1)(2n+1))/(2n) is 3n+9/2+3/(2n)

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

expand

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

3 n + \frac{9}{2} + \frac{3}{2 n}

Solution steps

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

Expand

3 (n + 1) (2 n + 1) : 6 n^{2} + 9 n + 3

= \frac{6 n ^{2} + 9 n + 3}{2 n}

Apply the fraction rule:

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

\frac{6 n ^{2} + 9 n + 3}{2 n} = \frac{6 n ^{2}}{2 n} + \frac{9 n}{2 n} + \frac{3}{2 n}

= \frac{6 n ^{2}}{2 n} + \frac{9 n}{2 n} + \frac{3}{2 n}

Cancel

\frac{6 n ^{2}}{2 n} : 3 n

= 3 n + \frac{9 n}{2 n} + \frac{3}{2 n}

Cancel

\frac{9 n}{2 n} : \frac{9}{2}

= 3 n + \frac{9}{2} + \frac{3}{2 n}

\frac{3 ( t + 1 ) ( t - 1 )}{t - 2}

(2 e^{2 r} sin (3 θ)) (s - 2 t)

(4 k - x m) (k z^{2} - x \frac{m z ^{2}}{4})

(\frac{7}{9} + \frac{2}{9})^{9}

\frac{1}{x - 2} - \frac{4}{x ^{2} - 4}

What is expand (3(n+1)(2n+1))/(2n) ?
The solution to expand (3(n+1)(2n+1))/(2n) is 3n+9/2+3/(2n)