簡約 xintercept(3x^3-4x^2-12x+16)/(3x^2+5x-2)

解

簡約

x in t erce pt \frac{3 x ^{3} - 4 x ^{2} - 12 x + 16}{3 x ^{2} + 5 x - 2}

\frac{e ^{2} c in x t ^{2} r p ( x - 2 ) ( 3 x - 4 )}{3 x - 1}

解答ステップ

x in t erce pt \frac{3 x ^{3} - 4 x ^{2} - 12 x + 16}{3 x ^{2} + 5 x - 2}

指数の規則を適用する:

a^{b} \cdot a^{c} = a^{b + c}

ee = e^{1 + 1}

= x in t rc e^{1 + 1} pt \frac{3 x ^{3} - 4 x ^{2} - 12 x + 16}{3 x ^{2} + 5 x - 2}

数を足す:

1 + 1 = 2

= x in t rc e^{2} pt \frac{3 x ^{3} - 4 x ^{2} - 12 x + 16}{3 x ^{2} + 5 x - 2}

指数の規則を適用する:

a^{b} \cdot a^{c} = a^{b + c}

tt = t^{1 + 1}

= x in rc e^{2} p t^{1 + 1} \frac{3 x ^{3} - 4 x ^{2} - 12 x + 16}{3 x ^{2} + 5 x - 2}

数を足す:

1 + 1 = 2

= x in rc e^{2} p t^{2} \frac{3 x ^{3} - 4 x ^{2} - 12 x + 16}{3 x ^{2} + 5 x - 2}

\frac{3 x ^{3} - 4 x ^{2} - 12 x + 16}{3 x ^{2} + 5 x - 2} = \frac{( 3 x - 4 ) ( x - 2 )}{3 x - 1}

= e^{2} c in \frac{( 3 x - 4 ) ( x - 2 )}{3 x - 1} x t^{2} r p

分数を乗じる:

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

= \frac{( 3 x - 4 ) ( x - 2 ) x in rc e ^{2} p t ^{2}}{3 x - 1}