展開する ((ln(x)+1)(1-ln(x))+ln(x))/((1-ln(x))^2)

解

展開する

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

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

解答ステップ

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

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

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

拡張

(ln (x) + 1) (1 - ln (x)) + ln (x) : 1 - ln^{2} (x) + ln (x)

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