What is (x/y-y/x)/(1/(6x^2)-1/(6y^2)) ?

The solution to (x/y-y/x)/(1/(6x^2)-1/(6y^2)) is -6xy

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simplify (x/y-y/x)/(1/(6x^2)-1/(6y^2))

simplify

\frac{\frac{x}{y} - \frac{y}{x}}{\frac{1}{6 x ^{2}} - \frac{1}{6 y ^{2}}}

- 6 x y

Solution steps

\frac{\frac{x}{y} - \frac{y}{x}}{\frac{1}{6 x ^{2}} - \frac{1}{6 y ^{2}}}

Join

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

= \frac{\frac{x ^{2} - y ^{2}}{x y}}{\frac{1}{6 x ^{2}} - \frac{1}{6 y ^{2}}}

Join

\frac{1}{6 x ^{2}} - \frac{1}{6 y ^{2}} : \frac{y ^{2} - x ^{2}}{6 x ^{2} y ^{2}}

= \frac{\frac{x ^{2} - y ^{2}}{x y}}{\frac{y ^{2} - x ^{2}}{6 x ^{2} y ^{2}}}

Apply the fraction rule:

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

= \frac{( x ^{2} - y ^{2} ) \cdot 6 x ^{2} y ^{2}}{x y ( y ^{2} - x ^{2} )}

Cancel

\frac{( x ^{2} - y ^{2} ) \cdot 6 x ^{2} y ^{2}}{x y ( y ^{2} - x ^{2} )} : - 6 x y

= - 6 x y

0.011 x^{2} + 0.0067 x + 0.2329 = 0.3015

\frac{1}{4} a = \frac{4}{15}

- 6 \leq 3 x < 9

2 x + 1 \leq - 6 or 2 x + 1 \geq 6

\frac{3.01}{3.01 - 3}

What is (x/y-y/x)/(1/(6x^2)-1/(6y^2)) ?
The solution to (x/y-y/x)/(1/(6x^2)-1/(6y^2)) is -6xy