展開する (ln^2(x)-ln(x)-2)/((x(ln(x)-4)))

解

展開する

\frac{ln ^{2} ( x ) - ln ( x ) - 2}{( x ( ln ( x ) - 4 ) )}

- \frac{2}{x ( ln ( x ) - 4 )}

解答ステップ

\frac{ln ^{2} ( x ) - ln ( x ) - 2}{( x ( ln ( x ) - 4 ) )}

対数の規則を適用する:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

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

= \frac{ln ^{2} ( \frac{x}{x} ) - 2}{x ( ln ( x ) - 4 )}

規則を適用

\frac{a}{a} = 1

= \frac{ln ^{2} ( 1 ) - 2}{x ( ln ( x ) - 4 )}

ln^{2} (1) = 0

= \frac{0 - 2}{x ( ln ( x ) - 4 )}

数を引く:

0 - 2 = - 2

= \frac{- 2}{x ( ln ( x ) - 4 )}

分数の規則を適用する:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{2}{x ( ln ( x ) - 4 )}