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

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

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

simplify

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

- y - x

Solution steps

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

Join

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

= \frac{\frac{y ^{2} - x ^{2}}{y x}}{\frac{1}{y} - \frac{1}{x}}

Join

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

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

Apply the fraction rule:

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

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

Cancel

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

= - y - x

x + 4 = 2 x + 1

4 (x + 2 y + z)^{2} - 9 (x - 2 y + z)^{2}

\frac{2 ^{9}}{2 ^{5}}

a^{- 8}

lo g_{8.5} (320)