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受欢迎的代数 >

展开 (-16/5)/(t+3)-(11/5)/(t-2)

解答

展开

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

解答

\frac{- 27 t - 1}{5 t ^{2} + 5 t - 30}

求解步骤

\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}

分解

5 t + 15 : 5 (t + 3)

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

分解

5 t - 10 : 5 (t - 2)

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

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

的最小公倍数:

5 (t + 3) (t - 2)

根据最小公倍数调整分式

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

因为分母相等，所以合并分式:

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

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

乘开

5 (t + 3) (t - 2) : 5 t^{2} + 5 t - 30

= \frac{- 16 ( t - 2 ) - 11 ( t + 3 )}{5 t ^{2} + 5 t - 30}

乘开

- 16 (t - 2) - 11 (t + 3) : - 27 t - 1

= \frac{- 27 t - 1}{5 t ^{2} + 5 t - 30}

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