簡約 ((2x^{-4}-6x^5+4x^2))/((2x^2))

解

簡約

\frac{( 2 x ^{- 4} - 6 x ^{5} + 4 x ^{2} )}{( 2 x ^{2} )}

\frac{1 - 3 x ^{9} + 2 x ^{6}}{x ^{6}}

解答ステップ

\frac{2 x ^{- 4} - 6 x ^{5} + 4 x ^{2}}{2 x ^{2}}

2 x^{- 4} = \frac{2}{x ^{4}}

= \frac{\frac{2}{x ^{4}} - 6 x ^{5} + 4 x ^{2}}{2 x ^{2}}

結合

\frac{2}{x ^{4}} - 6 x^{5} + 4 x^{2} : \frac{2 - 6 x ^{9} + 4 x ^{6}}{x ^{4}}

= \frac{\frac{2 - 6 x ^{9} + 4 x ^{6}}{x ^{4}}}{2 x ^{2}}

分数の規則を適用する:

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

= \frac{2 - 6 x ^{9} + 4 x ^{6}}{x ^{4} \cdot 2 x ^{2}}

因数

2 - 6 x^{9} + 4 x^{6} : 2 (1 - 3 x^{9} + 2 x^{6})

= \frac{2 ( 1 - 3 x ^{9} + 2 x ^{6} )}{x ^{4} \cdot 2 x ^{2}}

数を割る:

\frac{2}{2} = 1

= \frac{1 - 3 x ^{9} + 2 x ^{6}}{x ^{4} x ^{2}}

x^{4} x^{2} = x^{6}

= \frac{1 - 3 x ^{9} + 2 x ^{6}}{x ^{6}}