展开 (25(x+4)^2)/(x^2)

解答

展开

\frac{25 ( x + 4 ) ^{2}}{x ^{2}}

25 + \frac{200}{x} + \frac{400}{x ^{2}}

求解步骤

\frac{25 ( x + 4 ) ^{2}}{x ^{2}}

(x + 4)^{2} = x^{2} + 8 x + 16

= \frac{25 ( x ^{2} + 8 x + 16 )}{x ^{2}}

乘开

25 (x^{2} + 8 x + 16) : 25 x^{2} + 200 x + 400

= \frac{25 x ^{2} + 200 x + 400}{x ^{2}}

使用分式法则:

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

\frac{25 x ^{2} + 200 x + 400}{x ^{2}} = \frac{25 x ^{2}}{x ^{2}} + \frac{200 x}{x ^{2}} + \frac{400}{x ^{2}}

= \frac{25 x ^{2}}{x ^{2}} + \frac{200 x}{x ^{2}} + \frac{400}{x ^{2}}

消掉

\frac{25 x ^{2}}{x ^{2}} : 25

= 25 + \frac{200 x}{x ^{2}} + \frac{400}{x ^{2}}

消掉

\frac{200 x}{x ^{2}} : \frac{200}{x}

= 25 + \frac{200}{x} + \frac{400}{x ^{2}}

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