簡約 ((-x)/(x+y))+(ln(x^2+y^2)-2ln(x))

解

簡約

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

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

解答ステップ

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

対数の規則を適用する:

a lo g_{c} (b) = lo g_{c} (b^{a})

2 ln (x) = ln (x^{2})

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

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

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