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

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

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

expand

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

\frac{n}{4} + \frac{1}{2} + \frac{1}{4 n}

Solution steps

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

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

= \frac{n ^{2} + 2 n + 1}{4 n}

Apply the fraction rule:

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

\frac{n ^{2} + 2 n + 1}{4 n} = \frac{n ^{2}}{4 n} + \frac{2 n}{4 n} + \frac{1}{4 n}

= \frac{n ^{2}}{4 n} + \frac{2 n}{4 n} + \frac{1}{4 n}

Cancel

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

= \frac{n}{4} + \frac{2 n}{4 n} + \frac{1}{4 n}

Cancel

\frac{2 n}{4 n} : \frac{1}{2}

= \frac{n}{4} + \frac{1}{2} + \frac{1}{4 n}

\frac{( n ^{2} - 3 n - 2 ) ^{2}}{4}

\frac{n ( 3 n + 5 )}{3}

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

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

5 \cdot (2 x + 3) x + 54

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