展開する ((6x+25)(sqrt(6x+25)-5))/(6x^2)

解

展開する

\frac{( 6 x + 25 ) ( 6 x + 25 - 5 )}{6 x ^{2}}

\frac{6 x + 25}{x} - \frac{5}{x} + \frac{25 6 x + 25}{6 x ^{2}} - \frac{125}{6 x ^{2}}

解答ステップ

\frac{( 6 x + 25 ) ( 6 x + 25 - 5 )}{6 x ^{2}}

拡張

(6 x + 25) (6 x + 25 - 5) : 6 x 6 x + 25 - 30 x + 25 6 x + 25 - 125

= \frac{6 x 6 x + 25 - 30 x + 25 6 x + 25 - 125}{6 x ^{2}}

分数の規則を適用する:

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

\frac{6 x 6 x + 25 - 30 x + 25 6 x + 25 - 125}{6 x ^{2}} = \frac{6 x 6 x + 25}{6 x ^{2}} - \frac{30 x}{6 x ^{2}} + \frac{25 6 x + 25}{6 x ^{2}} - \frac{125}{6 x ^{2}}

= \frac{6 x 6 x + 25}{6 x ^{2}} - \frac{30 x}{6 x ^{2}} + \frac{25 6 x + 25}{6 x ^{2}} - \frac{125}{6 x ^{2}}

キャンセル

\frac{6 x 6 x + 25}{6 x ^{2}} : \frac{6 x + 25}{x}

= \frac{6 x + 25}{x} - \frac{30 x}{6 x ^{2}} + \frac{25 6 x + 25}{6 x ^{2}} - \frac{125}{6 x ^{2}}

キャンセル

\frac{30 x}{6 x ^{2}} : \frac{5}{x}

= \frac{6 x + 25}{x} - \frac{5}{x} + \frac{25 6 x + 25}{6 x ^{2}} - \frac{125}{6 x ^{2}}