展開する (-16/5)/(t+3)+(11/5)/(t-2)

解

展開する

\frac{- \frac{16}{5}}{t + 3} + \frac{\frac{11}{5}}{t - 2}

- \frac{t - 13}{t ^{2} + t - 6}

解答ステップ

\frac{- \frac{16}{5}}{t + 3} + \frac{\frac{11}{5}}{t - 2}

\frac{- \frac{16}{5}}{t + 3} = - \frac{16}{5 t + 15}

= - \frac{16}{5 t + 15} + \frac{\frac{11}{5}}{t - 2}

\frac{\frac{11}{5}}{t - 2} = \frac{11}{5 t - 10}

= - \frac{16}{5 t + 15} + \frac{11}{5 t - 10}

因数

5 t + 15 : 5 (t + 3)

= - \frac{16}{5 ( t + 3 )} + \frac{11}{5 t - 10}

因数

5 t - 10 : 5 (t - 2)

= - \frac{16}{5 ( t + 3 )} + \frac{11}{5 ( t - 2 )}

以下の最小公倍数:

5 (t + 3), 5 (t - 2) : 5 (t + 3) (t - 2)

LCMに基づいて分数を調整する

= - \frac{16 ( t - 2 )}{5 ( t + 3 ) ( t - 2 )} + \frac{11 ( t + 3 )}{5 ( t - 2 ) ( t + 3 )}

分母が等しいので, 分数を組み合わせる:

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

= \frac{- 16 ( t - 2 ) + 11 ( t + 3 )}{5 ( t + 3 ) ( t - 2 )}

因数

11 (t + 3) - 16 (t - 2) : - 5 (t - 13)

= - \frac{5 ( t - 13 )}{5 ( t + 3 ) ( t - 2 )}

数を割る:

\frac{5}{5} = 1

= - \frac{t - 13}{( t + 3 ) ( t - 2 )}

拡張

(t + 3) (t - 2) : t^{2} + t - 6

= - \frac{t - 13}{t ^{2} + t - 6}