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

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

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

expand

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

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

Solution steps

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

Expand

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

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

Apply the fraction rule:

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

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

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

Cancel

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

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

Cancel

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

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

(3 x + 2 y = 9.5) (x + y)

2 (x (x - 1))

(x - i)^{2} (x - 1 + i)^{2}

(x - 2 i) (x + 2 i) (x - 3 - i) (x - 3 + i)

2 (cot (x) - tan (x)) sin (2 x)

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