展开 ((40-k)(5+k))/(45)

解答

展开

\frac{( 40 - k ) ( 5 + k )}{45}

\frac{40}{9} + \frac{7 k}{9} - \frac{k ^{2}}{45}

求解步骤

\frac{( 40 - k ) ( 5 + k )}{45}

乘开

(40 - k) (5 + k) : 200 + 35 k - k^{2}

= \frac{200 + 35 k - k ^{2}}{45}

使用分式法则:

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

\frac{200 + 35 k - k ^{2}}{45} = \frac{200}{45} + \frac{35 k}{45} - \frac{k ^{2}}{45}

= \frac{200}{45} + \frac{35 k}{45} - \frac{k ^{2}}{45}

消掉

\frac{200}{45} : \frac{40}{9}

= \frac{40}{9} + \frac{35 k}{45} - \frac{k ^{2}}{45}

消掉

\frac{35 k}{45} : \frac{7 k}{9}

= \frac{40}{9} + \frac{7 k}{9} - \frac{k ^{2}}{45}

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