What is ((1/y+1/x))/(x/y-y/x) ?

The solution to ((1/y+1/x))/(x/y-y/x) is 1/(x-y)

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simplify ((1/y+1/x))/(x/y-y/x)

simplify

\frac{( \frac{1}{y} + \frac{1}{x} )}{\frac{x}{y} - \frac{y}{x}}

\frac{1}{x - y}

Solution steps

\frac{\frac{1}{y} + \frac{1}{x}}{\frac{x}{y} - \frac{y}{x}}

Join

\frac{1}{y} + \frac{1}{x} : \frac{x + y}{y x}

= \frac{\frac{x + y}{y x}}{\frac{x}{y} - \frac{y}{x}}

Join

\frac{x}{y} - \frac{y}{x} : \frac{x ^{2} - y ^{2}}{y x}

= \frac{\frac{x + y}{y x}}{\frac{x ^{2} - y ^{2}}{y x}}

Apply the fraction rule:

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

= \frac{( x + y ) y x}{y x ( x ^{2} - y ^{2} )}

Cancel

\frac{( x + y ) y x}{y x ( x ^{2} - y ^{2} )} : \frac{1}{x - y}

= \frac{1}{x - y}

- n + (- 4) - (- 4 n) + 6

2 (3 x + 3) - 4 (5 x - 3) = x (x - 3) - x (x + 5)

\frac{u ^{4 x + 1}}{u ^{x}}

0.25 a^{6} b^{2} - 0.6 a^{4} b^{4} + 0.36 a^{2} b^{6}

2 x^{2} - 12 x + 18 = 0

What is ((1/y+1/x))/(x/y-y/x) ?
The solution to ((1/y+1/x))/(x/y-y/x) is 1/(x-y)