What is expand (7(n+1)^2)/(4n) ?

The solution to expand (7(n+1)^2)/(4n) is (7n)/4+7/2+7/(4n)

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expand (7(n+1)^2)/(4n)

expand

\frac{7 ( n + 1 ) ^{2}}{4 n}

\frac{7 n}{4} + \frac{7}{2} + \frac{7}{4 n}

Solution steps

\frac{7 ( n + 1 ) ^{2}}{4 n}

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

= \frac{7 ( n ^{2} + 2 n + 1 )}{4 n}

Expand

7 (n^{2} + 2 n + 1) : 7 n^{2} + 14 n + 7

= \frac{7 n ^{2} + 14 n + 7}{4 n}

Apply the fraction rule:

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

\frac{7 n ^{2} + 14 n + 7}{4 n} = \frac{7 n ^{2}}{4 n} + \frac{14 n}{4 n} + \frac{7}{4 n}

= \frac{7 n ^{2}}{4 n} + \frac{14 n}{4 n} + \frac{7}{4 n}

Cancel

\frac{7 n ^{2}}{4 n} : \frac{7 n}{4}

= \frac{7 n}{4} + \frac{14 n}{4 n} + \frac{7}{4 n}

Cancel

\frac{14 n}{4 n} : \frac{7}{2}

= \frac{7 n}{4} + \frac{7}{2} + \frac{7}{4 n}

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

(x + h)^{2} + (x + h)

(6 x + \frac{1}{5})^{3}

(- x - cot (x)) sin (x)

\frac{( ( 1 - 4 x ) ^{2} - x ) ( x ^{2} + 1 )}{2 x - 3}

What is expand (7(n+1)^2)/(4n) ?
The solution to expand (7(n+1)^2)/(4n) is (7n)/4+7/2+7/(4n)