展開する (ln(\sqrt[4]{x(x+4)^3}))/(x+2)

解

展開する

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

\frac{ln ( x ^{4} + 12 x ^{3} + 48 x ^{2} + 64 x )}{4 x + 8}

解答ステップ

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

4 x (x + 4)^{3} = 4 x^{4} + 12 x^{3} + 48 x^{2} + 64 x

= \frac{ln ( 4 x ^{4} + 12 x ^{3} + 48 x ^{2} + 64 x )}{x + 2}

簡素化

ln (4 x^{4} + 12 x^{3} + 48 x^{2} + 64 x) : \frac{1}{4} ln (x^{4} + 12 x^{3} + 48 x^{2} + 64 x)

= \frac{\frac{1}{4} ln ( x ^{4} + 12 x ^{3} + 48 x ^{2} + 64 x )}{x + 2}

乗じる

\frac{1}{4} ln (x^{4} + 12 x^{3} + 48 x^{2} + 64 x) : \frac{ln ( x ^{4} + 12 x ^{3} + 48 x ^{2} + 64 x )}{4}

= \frac{\frac{l n ( x ^{4} + 12 x ^{3} + 48 x ^{2} + 64 x )}{4}}{x + 2}

分数の規則を適用する:

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

= \frac{ln ( x ^{4} + 12 x ^{3} + 48 x ^{2} + 64 x )}{4 ( x + 2 )}

拡張

4 (x + 2) : 4 x + 8

= \frac{ln ( x ^{4} + 12 x ^{3} + 48 x ^{2} + 64 x )}{4 x + 8}