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

The solution to (1/x-1/y)(1/x+1/y)(x/y-y/x) is ((y-x)(y+x)(x^2-y^2))/(x^3y^3)

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

simplify

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

\frac{( y - x ) ( y + x ) ( x ^{2} - y ^{2} )}{x ^{3} y ^{3}}

Solution steps

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

Join

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

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

Apply the fraction rule:

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

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

Simplify

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

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

Apply the fraction rule:

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

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

Simplify

x^{2} y^{2} x y : x^{3} y^{3}

= \frac{( y - x ) ( y + x ) ( x ^{2} - y ^{2} )}{x ^{3} y ^{3}}

(7 a + b)^{3}

6 a^{2} b^{3} + 12 a^{4} b

65 x^{3} - 35 x^{2} + 5 x

\frac{( x ^{2} + 5 x + 6 )}{( x + 3 )}

1 - \frac{\frac{( v + 3 )}{( 4 v + 24 )}}{2} + \frac{( 2 )}{( v + 6 )}

What is (1/x-1/y)(1/x+1/y)(x/y-y/x) ?
The solution to (1/x-1/y)(1/x+1/y)(x/y-y/x) is ((y-x)(y+x)(x^2-y^2))/(x^3y^3)