What is (1/q+q/p)/(p/q-1/p) ?

The solution to (1/q+q/p)/(p/q-1/p) is (p+q^2)/(p^2-q)

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

simplify

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

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

Solution steps

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

Join

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

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

Join

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

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

Apply the fraction rule:

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

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

Cancel

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

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

\frac{a + b}{6} - \frac{a - 2 b}{6}

9^{7}

3 m^{2} + 4 m - 4

9 p^{7} - 36 p^{5}

4 x^{2} = 2 x + 7

What is (1/q+q/p)/(p/q-1/p) ?
The solution to (1/q+q/p)/(p/q-1/p) is (p+q^2)/(p^2-q)