簡約 (2e^{2t}(2t-1)-4e^t)e^{-2t}

解

簡約

(2 e^{2 t} (2 t - 1) - 4 e^{t}) e^{- 2 t}

\frac{2 ( e ^{t} ( 2 t - 1 ) - 2 )}{e ^{t}}

解答ステップ

(2 e^{2 t} (2 t - 1) - 4 e^{t}) e^{- 2 t}

指数の規則を適用する:

a^{- b} = \frac{1}{a ^{b}}

= \frac{1}{e ^{2 t}} (- 4 e^{t} + 2 e^{2 t} (2 t - 1))

分数を乗じる:

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

= \frac{1 \cdot ( 2 e ^{2 t} ( 2 t - 1 ) - 4 e ^{t} )}{e ^{2 t}}

1 \cdot (2 e^{2 t} (2 t - 1) - 4 e^{t}) = 2 e^{2 t} (2 t - 1) - 4 e^{t}

= \frac{2 e ^{2 t} ( 2 t - 1 ) - 4 e ^{t}}{e ^{2 t}}

因数

2 e^{2 t} (2 t - 1) - 4 e^{t} : 2 e^{t} (e^{t} (- 1 + 2 t) - 2)

= \frac{2 e ^{t} ( e ^{t} ( - 1 + 2 t ) - 2 )}{e ^{2 t}}

キャンセル

\frac{2 e ^{t} ( e ^{t} ( - 1 + 2 t ) - 2 )}{e ^{2 t}} : \frac{2 ( e ^{t} ( - 1 + 2 t ) - 2 )}{e ^{t}}

= \frac{2 ( e ^{t} ( - 1 + 2 t ) - 2 )}{e ^{t}}

= \frac{2 ( e ^{t} ( 2 t - 1 ) - 2 )}{e ^{t}}