化简 (a-\frac{ab)/(a+b)}{a+(ab)/(a-b)}

解答

化简

\frac{a - \frac{ab}{a + b}}{a + \frac{ab}{a - b}}

\frac{a - b}{a + b}

求解步骤

\frac{a - \frac{ab}{a + b}}{a + \frac{ab}{a - b}}

合并

a - \frac{ab}{a + b} : \frac{a ^{2}}{a + b}

= \frac{\frac{a ^{2}}{a + b}}{a + \frac{ab}{a - b}}

合并

a + \frac{ab}{a - b} : \frac{a ^{2}}{a - b}

= \frac{\frac{a ^{2}}{a + b}}{\frac{a ^{2}}{a - b}}

使用分式法则:

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

= \frac{a ^{2} ( a - b )}{( a + b ) a ^{2}}

约分:

a^{2}

= \frac{a - b}{a + b}

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