展开 (7(n+1)^2)/(4n)

解答

展开

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

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

求解步骤

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

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

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

乘开

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

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

使用分式法则:

\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}

消掉

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

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

消掉

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

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

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