vereinfachen (1/q+q/p)/(p/q-1/p)

Lösung

vereinfachen

\frac{\frac{1}{q} + \frac{q}{p}}{\frac{p}{q} - \frac{1}{p}}

\frac{p + q ^{2}}{p ^{2} - q}

Schritte zur Lösung

\frac{\frac{1}{q} + \frac{q}{p}}{\frac{p}{q} - \frac{1}{p}}

Füge zusammen:

\frac{1}{q} + \frac{q}{p} : \frac{p + q ^{2}}{qp}

= \frac{\frac{p + q ^{2}}{qp}}{\frac{p}{q} - \frac{1}{p}}

Füge zusammen:

\frac{p}{q} - \frac{1}{p} : \frac{p ^{2} - q}{qp}

= \frac{\frac{p + q ^{2}}{qp}}{\frac{p ^{2} - q}{qp}}

Wende Bruchregel an:

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

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

Streiche

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

= \frac{p + q ^{2}}{p ^{2} - q}

s im pl i f y \frac{a + b}{6} - \frac{a - 2 b}{6}

s im pl i f y 9^{7}

f a c t or 9 p^{7} - 36 p^{5}

4 x^{2} = 2 x + 7

s im pl i f y - 88