What is (1/r+1/s)/(1/(r^2)-1/(s^2)) ?

The solution to (1/r+1/s)/(1/(r^2)-1/(s^2)) is (rs)/(s-r)

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simplify (1/r+1/s)/(1/(r^2)-1/(s^2))

simplify

\frac{\frac{1}{r} + \frac{1}{s}}{\frac{1}{r ^{2}} - \frac{1}{s ^{2}}}

\frac{rs}{s - r}

Solution steps

\frac{\frac{1}{r} + \frac{1}{s}}{\frac{1}{r ^{2}} - \frac{1}{s ^{2}}}

Join

\frac{1}{r} + \frac{1}{s} : \frac{s + r}{rs}

= \frac{\frac{s + r}{rs}}{\frac{1}{r ^{2}} - \frac{1}{s ^{2}}}

Join

\frac{1}{r ^{2}} - \frac{1}{s ^{2}} : \frac{s ^{2} - r ^{2}}{r ^{2} s ^{2}}

= \frac{\frac{s + r}{rs}}{\frac{s ^{2} - r ^{2}}{r ^{2} s ^{2}}}

Apply the fraction rule:

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

= \frac{( s + r ) r ^{2} s ^{2}}{rs ( s ^{2} - r ^{2} )}

Cancel

\frac{( s + r ) r ^{2} s ^{2}}{rs ( s ^{2} - r ^{2} )} : \frac{rs}{s - r}

= \frac{rs}{s - r}

4 = - \frac{5}{4} (- 6) + b

(2 i)^{5} \cdot (i 6)^{2}

410 \cdot 36

- 4 x + 5 = (x - 2)^{2} + 1

What is (1/r+1/s)/(1/(r^2)-1/(s^2)) ?
The solution to (1/r+1/s)/(1/(r^2)-1/(s^2)) is (rs)/(s-r)