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

The solution to expand (2(n+1)(2n+1))/n is 4n+6+2/n

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

expand

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

4 n + 6 + \frac{2}{n}

Solution steps

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

Expand

2 (n + 1) (2 n + 1) : 4 n^{2} + 6 n + 2

= \frac{4 n ^{2} + 6 n + 2}{n}

Apply the fraction rule:

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

\frac{4 n ^{2} + 6 n + 2}{n} = \frac{4 n ^{2}}{n} + \frac{6 n}{n} + \frac{2}{n}

= \frac{4 n ^{2}}{n} + \frac{6 n}{n} + \frac{2}{n}

Cancel

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

= 4 n + \frac{6 n}{n} + \frac{2}{n}

Cancel

\frac{6 n}{n} : 6

= 4 n + 6 + \frac{2}{n}

(2^{4}) (2^{3})

\frac{x - 1}{( x + 1 ) ( x + 2 )}

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

2 (8 - 3 e)

n (n - 1)!

What is expand (2(n+1)(2n+1))/n ?
The solution to expand (2(n+1)(2n+1))/n is 4n+6+2/n