展开 (64(x+1)(2x+1))/(x^2)

解答

展开

\frac{64 ( x + 1 ) ( 2 x + 1 )}{x ^{2}}

128 + \frac{192}{x} + \frac{64}{x ^{2}}

求解步骤

\frac{64 ( x + 1 ) ( 2 x + 1 )}{x ^{2}}

乘开

64 (x + 1) (2 x + 1) : 128 x^{2} + 192 x + 64

= \frac{128 x ^{2} + 192 x + 64}{x ^{2}}

使用分式法则:

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

\frac{128 x ^{2} + 192 x + 64}{x ^{2}} = \frac{128 x ^{2}}{x ^{2}} + \frac{192 x}{x ^{2}} + \frac{64}{x ^{2}}

= \frac{128 x ^{2}}{x ^{2}} + \frac{192 x}{x ^{2}} + \frac{64}{x ^{2}}

消掉

\frac{128 x ^{2}}{x ^{2}} : 128

= 128 + \frac{192 x}{x ^{2}} + \frac{64}{x ^{2}}

消掉

\frac{192 x}{x ^{2}} : \frac{192}{x}

= 128 + \frac{192}{x} + \frac{64}{x ^{2}}

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