What is expand (81(n+1)^2)/(4n^2) ?

The solution to expand (81(n+1)^2)/(4n^2) is 81/4+(81)/(2n)+(81)/(4n^2)

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expand (81(n+1)^2)/(4n^2)

expand

\frac{81 ( n + 1 ) ^{2}}{4 n ^{2}}

\frac{81}{4} + \frac{81}{2 n} + \frac{81}{4 n ^{2}}

Solution steps

\frac{81 ( n + 1 ) ^{2}}{4 n ^{2}}

(n + 1)^{2} = n^{2} + 2 n + 1

= \frac{81 ( n ^{2} + 2 n + 1 )}{4 n ^{2}}

Expand

81 (n^{2} + 2 n + 1) : 81 n^{2} + 162 n + 81

= \frac{81 n ^{2} + 162 n + 81}{4 n ^{2}}

Apply the fraction rule:

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

\frac{81 n ^{2} + 162 n + 81}{4 n ^{2}} = \frac{81 n ^{2}}{4 n ^{2}} + \frac{162 n}{4 n ^{2}} + \frac{81}{4 n ^{2}}

= \frac{81 n ^{2}}{4 n ^{2}} + \frac{162 n}{4 n ^{2}} + \frac{81}{4 n ^{2}}

Cancel

\frac{81 n ^{2}}{4 n ^{2}} : \frac{81}{4}

= \frac{81}{4} + \frac{162 n}{4 n ^{2}} + \frac{81}{4 n ^{2}}

Cancel

\frac{162 n}{4 n ^{2}} : \frac{81}{2 n}

= \frac{81}{4} + \frac{81}{2 n} + \frac{81}{4 n ^{2}}

\frac{1}{( s + 2 ) ( s ^{2} + 2 s + 3 )}

(1 + ln (x)) d x + (1 + ln (y)) d y

\frac{x + 8}{( x - 5 ) ( x + 5 )}

cos (2) (π - x)

\frac{2}{( x ^{6} + x ^{2} + 1 ) ^{2}}

What is expand (81(n+1)^2)/(4n^2) ?
The solution to expand (81(n+1)^2)/(4n^2) is 81/4+(81)/(2n)+(81)/(4n^2)