化简 (p-2/q)(p^2+(2p)/q+4/(q^2))

解答

化简

(p - \frac{2}{q}) (p^{2} + \frac{2 p}{q} + \frac{4}{q ^{2}})

\frac{( pq - 2 ) ( p ^{2} q ^{2} + 2 pq + 4 )}{q ^{3}}

求解步骤

(p - \frac{2}{q}) (p^{2} + \frac{2 p}{q} + \frac{4}{q ^{2}})

合并

p - \frac{2}{q} : \frac{pq - 2}{q}

= \frac{pq - 2}{q} (p^{2} + \frac{2 p}{q} + \frac{4}{q ^{2}})

使用分式法则:

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

= \frac{( pq - 2 ) ( p ^{2} + \frac{2 p}{q} + \frac{4}{q ^{2}} )}{q}

化简

(pq - 2) (p^{2} + \frac{2 p}{q} + \frac{4}{q ^{2}}) : \frac{( pq - 2 ) ( p ^{2} q ^{2} + 2 pq + 4 )}{q ^{2}}

= \frac{\frac{( pq - 2 ) ( p ^{2} q ^{2} + 2 pq + 4 )}{q ^{2}}}{q}

使用分式法则:

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

= \frac{( pq - 2 ) ( p ^{2} q ^{2} + 2 pq + 4 )}{q ^{2} q}

化简

q^{2} q : q^{3}

= \frac{( pq - 2 ) ( p ^{2} q ^{2} + 2 pq + 4 )}{q ^{3}}

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