What is expand (205(n+1)(2n+1))/(2n^2) ?

The solution to expand (205(n+1)(2n+1))/(2n^2) is 205+(615)/(2n)+(205)/(2n^2)

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expand (205(n+1)(2n+1))/(2n^2)

expand

\frac{205 ( n + 1 ) ( 2 n + 1 )}{2 n ^{2}}

205 + \frac{615}{2 n} + \frac{205}{2 n ^{2}}

Solution steps

\frac{205 ( n + 1 ) ( 2 n + 1 )}{2 n ^{2}}

Expand

205 (n + 1) (2 n + 1) : 410 n^{2} + 615 n + 205

= \frac{410 n ^{2} + 615 n + 205}{2 n ^{2}}

Apply the fraction rule:

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

\frac{410 n ^{2} + 615 n + 205}{2 n ^{2}} = \frac{410 n ^{2}}{2 n ^{2}} + \frac{615 n}{2 n ^{2}} + \frac{205}{2 n ^{2}}

= \frac{410 n ^{2}}{2 n ^{2}} + \frac{615 n}{2 n ^{2}} + \frac{205}{2 n ^{2}}

Cancel

\frac{410 n ^{2}}{2 n ^{2}} : 205

= 205 + \frac{615 n}{2 n ^{2}} + \frac{205}{2 n ^{2}}

Cancel

\frac{615 n}{2 n ^{2}} : \frac{615}{2 n}

= 205 + \frac{615}{2 n} + \frac{205}{2 n ^{2}}

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What is expand (205(n+1)(2n+1))/(2n^2) ?
The solution to expand (205(n+1)(2n+1))/(2n^2) is 205+(615)/(2n)+(205)/(2n^2)