化简 1250-0.5x^2+(100(2500-x))/(0.02x+1)

解答

化简

1250 - 0.5 x^{2} + \frac{100 ( 2500 - x )}{0.02 x + 1}

\frac{- 0.01 x ^{3} - 0.5 x ^{2} - 75 x + 251250}{0.02 x + 1}

求解步骤

1250 - 0.5 x^{2} + \frac{100 ( 2500 - x )}{0.02 x + 1}

将

1250

转换为分数

: \frac{1250 ( 0.02 x + 1 )}{0.02 x + 1}

将

0.5 x^{2}

转换为分数

: \frac{0.5 x ^{2} ( 0.02 x + 1 )}{0.02 x + 1}

= \frac{1250 ( 0.02 x + 1 )}{0.02 x + 1} - \frac{0.5 x ^{2} ( 0.02 x + 1 )}{0.02 x + 1} + \frac{100 ( 2500 - x )}{0.02 x + 1}

使用分式法则:

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

= \frac{1250 ( 0.02 x + 1 ) - 0.5 x ^{2} ( 0.02 x + 1 ) + 100 ( 2500 - x )}{0.02 x + 1}

化简

1250 (0.02 x + 1) - 0.5 x^{2} (0.02 x + 1) + 100 (2500 - x) : - 0.01 x^{3} - 0.5 x^{2} - 75 x + 251250

= \frac{- 0.01 x ^{3} - 0.5 x ^{2} - 75 x + 251250}{0.02 x + 1}

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