展開する (ln(x)-1)/((ln(x))^2)+1

解

展開する

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

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

解答ステップ

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

分数の規則を適用する:

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

\frac{ln ( x ) - 1}{ln ^{2} ( x )} = \frac{ln ( x )}{ln ^{2} ( x )} - \frac{1}{ln ^{2} ( x )}

= \frac{ln ( x )}{ln ^{2} ( x )} - \frac{1}{ln ^{2} ( x )} + 1

キャンセル

\frac{ln ( x )}{ln ^{2} ( x )} : \frac{1}{ln ( x )}

= \frac{1}{ln ( x )} - \frac{1}{ln ^{2} ( x )} + 1