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受欢迎的代数 >

化简 (x/y-y/x)/(1/(6x^2)-1/(6y^2))

解答

化简

\frac{\frac{x}{y} - \frac{y}{x}}{\frac{1}{6 x ^{2}} - \frac{1}{6 y ^{2}}}

解答

- 6 x y

求解步骤

\frac{\frac{x}{y} - \frac{y}{x}}{\frac{1}{6 x ^{2}} - \frac{1}{6 y ^{2}}}

合并

\frac{x}{y} - \frac{y}{x} : \frac{x ^{2} - y ^{2}}{x y}

= \frac{\frac{x ^{2} - y ^{2}}{x y}}{\frac{1}{6 x ^{2}} - \frac{1}{6 y ^{2}}}

合并

\frac{1}{6 x ^{2}} - \frac{1}{6 y ^{2}} : \frac{y ^{2} - x ^{2}}{6 x ^{2} y ^{2}}

= \frac{\frac{x ^{2} - y ^{2}}{x y}}{\frac{y ^{2} - x ^{2}}{6 x ^{2} y ^{2}}}

使用分式法则:

\frac{\frac{a}{b}}{\frac{c}{d}} = \frac{a \cdot d}{b \cdot c}

= \frac{( x ^{2} - y ^{2} ) \cdot 6 x ^{2} y ^{2}}{x y ( y ^{2} - x ^{2} )}

消掉

\frac{( x ^{2} - y ^{2} ) \cdot 6 x ^{2} y ^{2}}{x y ( y ^{2} - x ^{2} )} : - 6 x y

= - 6 x y

流行的例子

0.011x^2+0.0067x+0.2329=0.3015

0.011 x^{2} + 0.0067 x + 0.2329 = 0.3015

化简 (3.01)/(3.01-3)

s im pl i f y \frac{3.01}{3.01 - 3}

化简 3/4+1/3+1/6

s im pl i f y \frac{3}{4} + \frac{1}{3} + \frac{1}{6}

2 m^{2} + 7 m - 22 = 0

0.6 = \frac{n}{5}