簡約 (2/3 m-1/2 m+1)+(-1/2 m^2+2/3 m-1)

解

簡約

(\frac{2}{3} m - \frac{1}{2} m + 1) + (- \frac{1}{2} m^{2} + \frac{2}{3} m - 1)

\frac{5}{6} m - \frac{1}{2} m^{2}

解答ステップ

(\frac{2}{3} m - \frac{1}{2} m + 1) + (- \frac{1}{2} m^{2} + \frac{2}{3} m - 1)

簡素化

(\frac{2}{3} m - \frac{1}{2} m + 1) + (- \frac{1}{2} m^{2} + \frac{2}{3} m - 1) : \frac{2}{3} m - \frac{1}{2} m + 1 - \frac{1}{2} m^{2} + \frac{2}{3} m - 1

= \frac{2}{3} m - \frac{1}{2} m + 1 - \frac{1}{2} m^{2} + \frac{2}{3} m - 1

条件のようなグループ

= \frac{2}{3} m + \frac{2}{3} m - \frac{1}{2} m - \frac{1}{2} m^{2} + 1 - 1

類似した元を足す:

\frac{2}{3} m + \frac{2}{3} m = 2 \cdot \frac{2}{3} m

= 2 \cdot \frac{2}{3} m - \frac{1}{2} m - \frac{1}{2} m^{2} + 1 - 1

共通項をくくり出す

m

= m (2 \cdot \frac{2}{3} - \frac{1}{2}) - \frac{1}{2} m^{2} + 1 - 1

数を引く:

1 - 1 = 0

= m (2 \cdot \frac{2}{3} - \frac{1}{2}) - \frac{1}{2} m^{2}

2 \cdot \frac{2}{3} - \frac{1}{2} = \frac{5}{6}

= m \frac{5}{6} - \frac{1}{2} m^{2}

= \frac{5}{6} m - \frac{1}{2} m^{2}