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

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

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

simplify

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

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

Solution steps

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

Join

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

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

Apply the fraction rule:

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

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

Simplify

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

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

Apply the fraction rule:

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

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

Simplify

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

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

(cos (2 t) - sin (2 t))^{2}

(i + 2)^{5}

(\frac{1}{4} x^{2} y + \frac{x}{y})^{10}

\frac{( 10 tan ^{2} ( x ) + 10 sec ( x ) )}{tan ( x ) ( 1 + sec ( x ) )}

(1 - \frac{x}{4}) (1 + 2 x)^{6}

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